Kyoto Journal of Mathematics Articles (Project Euclid)
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The latest articles from Kyoto Journal of Mathematics on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTFri, 22 Apr 2011 13:49 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Toeplitz CAR flows and type I factorizations
http://projecteuclid.org/euclid.kjm/1271187735
<strong>Masaki Izumi</strong>, <strong>R. Srinivasan</strong><p><strong>Source: </strong>Kyoto J. Math., Volume 50, Number 1, 1--32.</p><p><strong>Abstract:</strong><br/>
Toeplitz CAR flows are a class of $E_{0}$ -semigroups including the first type III example constructed by R. T. Powers. We show that the Toeplitz CAR flows contain uncountably many mutually non-cocycle-conjugate $E_{0}$ -semigroups of type III. We also generalize the type III criterion for Toeplitz canonical anticommutation relation (CAR) flows employed by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows are always either of type I or type III.
</p>projecteuclid.org/euclid.kjm/1271187735_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTThe moment map on symplectic vector space and oscillator representationhttp://projecteuclid.org/euclid.kjm/1493798414<strong>Takashi Hashimoto</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 3, 553--583.</p><p><strong>Abstract:</strong><br/>
Let $G$ denote $\operatorname{Sp}(n,\mathbb{R})$ , $\mathrm{U}(p,q)$ , or $\mathrm{O}^{*}(2n)$ . The main aim of this article is to show that the canonical quantization of the moment map on a symplectic $G$ -vector space $(W,\omega)$ naturally gives rise to the oscillator (or Segal–Shale–Weil) representation of $\mathfrak{g}:=\operatorname{Lie}(G)\otimes\mathbb{C}$ . More precisely, after taking a complex Lagrangian subspace $V$ of the complexification of $W$ , we assign an element of the Weyl algebra for $V$ to $\langle \mu,X\rangle $ for each $X\in\mathfrak{g}$ , which we denote by $\langle \widehat{\mu},X\rangle $ . Then we show that the map $X\mapsto\mathrm{i}\langle \widehat{\mu},X\rangle $ gives a representation of $\mathfrak{g}$ . With a suitable choice of $V$ in each case, the representation coincides with the oscillator representation of $\mathfrak{g}$ .
</p>projecteuclid.org/euclid.kjm/1493798414_20170725040241Tue, 25 Jul 2017 04:02 EDTQuadratic numerical semigroups and the Koszul propertyhttp://projecteuclid.org/euclid.kjm/1492826434<strong>Jürgen Herzog</strong>, <strong>Dumitru I. Stamate</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 3, 585--612.</p><p><strong>Abstract:</strong><br/>
Let $H$ be a numerical semigroup. We give effective bounds for the multiplicity $e(H)$ when the associated graded ring $\operatorname{gr}_{\mathfrak{m}}K[H]$ is defined by quadrics. We classify Koszul complete intersection semigroups in terms of gluings. Furthermore, for several classes of numerical semigroups considered in the literature (arithmetic, compound, special almost-complete intersections, $3$ -semigroups, symmetric or pseudosymmetric $4$ -semigroups) we classify those which are Koszul.
</p>projecteuclid.org/euclid.kjm/1492826434_20170725040241Tue, 25 Jul 2017 04:02 EDTHamiltonian $C^{0}$ -continuity of Lagrangian capacity on the cotangent bundlehttp://projecteuclid.org/euclid.kjm/1492826433<strong>Yong-Geun Oh</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 3, 613--636.</p><p><strong>Abstract:</strong><br/>
Partially motivated by the study of topological Hamiltonian dynamics, we prove the following $C^{0}$ -continuity of the Lagrangian capacity function $\gamma^{\mathrm{lag}}$ :
\[\gamma^{\mathrm{lag}}(\phi_{H}^{1}(o_{N})):=\rho^{\mathrm{lag}}(H;1)-\rho^{\mathrm{lag}}(H;[pt]^{\#})\to0,\] as $\phi_{H}^{1}\to id$ , provided the $H$ ’s satisfy $\operatorname{supp}X_{H}\subset D^{R}(T^{*}N)\setminus o_{B}$ for some $R\gt 0$ and a closed subset $B\subset N$ with nonempty interior. We also provide an estimate of the capacity in terms of the $C^{0}$ -distance of $d_{C^{0}}(\phi_{H}^{1},id)$ and the subset $B\subset N$ relative to $T^{*}N$ .
</p>projecteuclid.org/euclid.kjm/1492826433_20170725040241Tue, 25 Jul 2017 04:02 EDTOn the doubly Feller property of resolventhttp://projecteuclid.org/euclid.kjm/1492194850<strong>Mila Kurniawaty</strong>, <strong>Kazuhiro Kuwae</strong>, <strong>Kaneharu Tsuchida</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 3, 637--654.</p><p><strong>Abstract:</strong><br/>
In this article, we show the stability of the doubly Feller property of the resolvent for Markov processes, generalizing a work by Kai-Lai Chung on the stability of the doubly Feller property of a semigroup with multiplicative functionals. The stability of the doubly Feller property of the resolvent under time change is also presented.
</p>projecteuclid.org/euclid.kjm/1492194850_20170725040241Tue, 25 Jul 2017 04:02 EDTWhen are the Rees algebras of parameter ideals almost Gorenstein graded rings?http://projecteuclid.org/euclid.kjm/1492194851<strong>Shiro Goto</strong>, <strong>Mehran Rahimi</strong>, <strong>Naoki Taniguchi</strong>, <strong>Hoang Le Truong</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 3, 655--666.</p><p><strong>Abstract:</strong><br/>
Let $A$ be a Cohen–Macaulay local ring with $\dim A=d\ge3$ , possessing the canonical module $\mathrm{K}_{A}$ . Let $a_{1},a_{2},\ldots,a_{r}$ $(3\le r\le d)$ be a subsystem of parameters of $A$ , and set $Q=(a_{1},a_{2},\ldots,a_{r})$ . We show that if the Rees algebra $\mathcal{R}(Q)$ of $Q$ is an almost Gorenstein graded ring, then $A$ is a regular local ring and $a_{1},a_{2},\ldots,a_{r}$ is a part of a regular system of parameters of $A$ .
</p>projecteuclid.org/euclid.kjm/1492194851_20170725040241Tue, 25 Jul 2017 04:02 EDTActions of locally compact (quantum) groups on ternary rings of operators, their crossed products, and generalized Poisson boundarieshttp://projecteuclid.org/euclid.kjm/1493798413<strong>Pekka Salmi</strong>, <strong>Adam Skalski</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 3, 667--691.</p><p><strong>Abstract:</strong><br/>
Actions of locally compact groups and quantum groups on W $^{*}$ -ternary rings of operators are discussed, and related crossed products are introduced. The results generalize those for von Neumann algebraic actions with proofs based mostly on passing to the linking von Neumann algebra. They are motivated by the study of fixed-point spaces for convolution operators generated by contractive, not necessarily positive measures, both in the classical and in the quantum context.
</p>projecteuclid.org/euclid.kjm/1493798413_20170725040241Tue, 25 Jul 2017 04:02 EDTThe approximate pseudorandom walk accompanied by the pseudostochastic process corresponding to a higher-order heat-type equationhttps://projecteuclid.org/euclid.kjm/1496973625<strong>Tadashi Nakajima</strong>, <strong>Sadao Sato</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 4, 693--716.</p><p><strong>Abstract:</strong><br/>
As is well known, a standard random walk is approximate to the stochastic process corresponding to the heat equation. Lachal constructed the approximate pseudorandom walk which is accompanied by the pseudostochastic process corresponding to an even-order heat-type equation. We have two purposes for this article. The first is to construct the approximate pseudorandom walk which is accompanied by the pseudostochastic process corresponding to an odd-order heat-type equation. The other is to propose a construction method for the approximate pseudorandom walk which is accompanied by the pseudostochastic process corresponding to an even-order heat-type equation. This method is different from that of Lachal.
</p>projecteuclid.org/euclid.kjm/1496973625_20171117220707Fri, 17 Nov 2017 22:07 ESTRegular functions on spherical nilpotent orbits in complex symmetric pairs: Classical non-Hermitian caseshttps://projecteuclid.org/euclid.kjm/1504080147<strong>Paolo Bravi</strong>, <strong>Rocco Chirivî</strong>, <strong>Jacopo Gandini</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 4, 717--787.</p><p><strong>Abstract:</strong><br/>
Given a classical semisimple complex algebraic group $G$ and a symmetric pair $(G,K)$ of non-Hermitian type, we study the closures of the spherical nilpotent $K$ -orbits in the isotropy representation of $K$ . For all such orbit closures, we study the normality, and we describe the $K$ -module structure of the ring of regular functions of the normalizations.
</p>projecteuclid.org/euclid.kjm/1504080147_20171117220707Fri, 17 Nov 2017 22:07 ESTOn the geometry of the Lehn–Lehn–Sorger–van Straten eightfoldhttps://projecteuclid.org/euclid.kjm/1496973624<strong>Evgeny Shinder</strong>, <strong>Andrey Soldatenkov</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 4, 789--806.</p><p><strong>Abstract:</strong><br/>
In this article we make a few remarks about the geometry of the holomorphic symplectic manifold $Z$ constructed by Lehn, Lehn, Sorger, and van Straten as a two-step contraction of the variety of twisted cubic curves on a cubic fourfold $Y\subset\mathbb{P}^{5}$ . We show that $Z$ is birational to a component of the moduli space of stable sheaves in the Calabi–Yau subcategory of the derived category of $Y$ . Using this description we deduce that the twisted cubics contained in a hyperplane section $Y_{H}=Y\cap H$ of $Y$ give rise to a Lagrangian subvariety $Z_{H}\subset Z$ . For a generic choice of the hyperplane, $Z_{H}$ is birational to the theta-divisor in the intermediate Jacobian $\mathrm{J}(Y_{H})$ .
</p>projecteuclid.org/euclid.kjm/1496973624_20171117220707Fri, 17 Nov 2017 22:07 ESTLattice multipolygonshttps://projecteuclid.org/euclid.kjm/1498096939<strong>Akihiro Higashitani</strong>, <strong>Mikiya Masuda</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 4, 807--828.</p><p><strong>Abstract:</strong><br/>
We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $\mathbb{Z}^{2}$ . We first prove a formula on the rotation number of a unimodular sequence in $\mathbb{Z}^{2}$ . This formula implies the generalized twelve-point theorem of Poonen and Rodriguez-Villegas. We then introduce the notion of lattice multipolygons, which is a generalization of lattice polygons, state the generalized Pick’s formula, and discuss the classification of Ehrhart polynomials of lattice multipolygons and also of several natural subfamilies of lattice multipolygons.
</p>projecteuclid.org/euclid.kjm/1498096939_20171117220707Fri, 17 Nov 2017 22:07 ESTThe moduli of representations of degree $2$https://projecteuclid.org/euclid.kjm/1497600015<strong>Kazunori Nakamoto</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 57, Number 4, 829--902.</p><p><strong>Abstract:</strong><br/>
There are six types of $2$ -dimensional representations in general. For any groups and any monoids, we can construct the moduli of $2$ -dimensional representations for each type: the moduli of absolutely irreducible representations, representations with Borel mold, representations with semisimple mold, representations with unipotent mold, representations with unipotent mold over ${\Bbb{F}}_{2}$ , and representations with scalar mold. We can also construct them for any associative algebras.
</p>projecteuclid.org/euclid.kjm/1497600015_20171117220707Fri, 17 Nov 2017 22:07 ESTThe cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplicationhttps://projecteuclid.org/euclid.kjm/1518685212<strong>Takashi Hara</strong>, <strong>Tadashi Ochiai</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 100 pages.</p><p><strong>Abstract:</strong><br/>
We deduce the cyclotomic Iwasawa main conjecture for Hilbert modular cusp forms with complex multiplication from the multivariable main conjecture for CM number fields. To this end, we study in detail the behavior of the $p$ -adic $L$ -functions and the Selmer groups attached to CM number fields under specialization procedures.
</p>projecteuclid.org/euclid.kjm/1518685212_20180215040027Thu, 15 Feb 2018 04:00 ESTClassifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagramhttps://projecteuclid.org/euclid.kjm/1513674221<strong>Kazuya Kato</strong>, <strong>Chikara Nakayama</strong>, <strong>Sampei Usui</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 138 pages.</p><p><strong>Abstract:</strong><br/>
We complete the construction of the fundamental diagram of various partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. The diagram includes the space of nilpotent orbits, the space of $\mathrm{SL}(2)$ -orbits, and the space of Borel–Serre orbits. We give amplifications of this fundamental diagram and amplify the relations of these spaces. We describe how this work is useful in understanding asymptotic behaviors of Beilinson regulators and of local height pairings in degeneration. We discuss mild degenerations in which regulators converge.
</p>projecteuclid.org/euclid.kjm/1513674221_20180215040027Thu, 15 Feb 2018 04:00 ESTOn a relation between the self-linking number and the braid index of closed braids in open bookshttps://projecteuclid.org/euclid.kjm/1510283180<strong>Tetsuya Ito</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 34 pages.</p><p><strong>Abstract:</strong><br/>
We prove a generalization of the Jones–Kawamuro conjecture that relates the self-linking number and the braid index of closed braids, for planar open books with certain additional conditions and modifications. We show that our result is optimal in some sense by giving several examples that do not satisfy a naive generalization of the Jones–Kawamuro conjecture.
</p>projecteuclid.org/euclid.kjm/1510283180_20180215040027Thu, 15 Feb 2018 04:00 ESTThe étale cohomology of the general linear group over a finite field and the Dickson algebrahttps://projecteuclid.org/euclid.kjm/1508378580<strong>Michishige Tezuka</strong>, <strong>Nobuaki Yagita</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 20 pages.</p><p><strong>Abstract:</strong><br/>
Let $p\neq\ell$ be primes. We study the étale cohomology $H^{*}_{\text{\'{e}t}}(\mathrm{BGL}_{n}(\mathbb{F}_{p^{s}});\mathbb{Z}/{\ell})$ by using the stratification methods from Molina-Rojas and Vistoli. To compute this cohomology, we use the Dickson algebra and the Drinfeld space.
</p>projecteuclid.org/euclid.kjm/1508378580_20180215040027Thu, 15 Feb 2018 04:00 ESTOn the distinguished spectrum of $\operatorname{Sp}_{2n}$ with respect to $\operatorname{Sp}_{n}\times\operatorname{Sp}_{n}$https://projecteuclid.org/euclid.kjm/1507600817<strong>Erez Moshe Lapid</strong>, <strong>Omer Offen</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 71 pages.</p><p><strong>Abstract:</strong><br/>
Given a reductive group $G$ and a reductive subgroup $H$ , both defined over a number field $F$ , we introduce the notion of the $H$ -distinguished automorphic spectrum of $G$ and analyze it for the pairs $(\operatorname{GL}_{2n},\operatorname{Sp}_{n})$ and $(\operatorname{Sp}_{2n},\operatorname{Sp}_{n}\times\operatorname{Sp}_{n})$ . In the first case we give a complete description by using results of Jacquet and Rallis as well as Offen and Yamana. In the second case we give an upper bound, generalizing vanishing results of Ash, Ginzburg, and Rallis, and a lower bound, extending results of Ginzburg, Rallis, and Soudry.
</p>projecteuclid.org/euclid.kjm/1507600817_20180215040027Thu, 15 Feb 2018 04:00 ESTCoefficient estimates of analytic endomorphisms of the unit disk fixing a point with applications to concave functionshttps://projecteuclid.org/euclid.kjm/1496973623<strong>Rintaro Ohno</strong>, <strong>Toshiyuki Sugawa</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 15 pages.</p><p><strong>Abstract:</strong><br/>
In this article, we discuss the coefficient regions of analytic self-maps of the unit disk with a prescribed fixed point. As an application, we solve the Fekete–Szegő problem for normalized concave functions with a pole in the unit disk.
</p>projecteuclid.org/euclid.kjm/1496973623_20180215040027Thu, 15 Feb 2018 04:00 ESTCanonical Kähler metrics and arithmetics: Generalizing Faltings heightshttps://projecteuclid.org/euclid.kjm/1520046287<strong>Yuji Odaka</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 46 pages.</p><p><strong>Abstract:</strong><br/>
We extend the Faltings modular heights of Abelian varieties to general arithmetic varieties, show direct relations with the Kähler–Einstein geometry, the minimal model program, and Bost–Zhang’s heights and give some applications. Along the way, we propose the “arithmetic Yau–Tian–Donaldson conjecture” (the equivalence of a purely arithmetic property of a variety and its metrical property) and partially confirm it.
</p>projecteuclid.org/euclid.kjm/1520046287_20180302220502Fri, 02 Mar 2018 22:05 ESTNote on strongly hyperbolic systems with involutive characteristicshttps://projecteuclid.org/euclid.kjm/1520240411<strong>Guy Métivier</strong>, <strong>Tatsuo Nishitani</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 14 pages.</p><p><strong>Abstract:</strong><br/>
We consider the Cauchy problem in $L^{2}$ for first-order systems. A necessary condition is that the system must be uniformly diagonalizable or, equivalently, that it admits a bounded symmetrizer. A sufficient condition is that it admits a smooth (Lipschitz) symmetrizer, which is true when the system is diagonalizable with eigenvalues of constant multiplicities. Counterexamples show that uniform diagonalizability is not sufficient in general for systems with variable coefficients, and they indicate that the symplectic properties of the set $\Sigma$ of the singular points of the characteristic variety are important. In this article, we give a new class of systems for which the Cauchy problem is well-posed in $L^{2}$ . The main assumption is that $\Sigma$ is a smooth involutive manifold and the system is transversally strictly hyperbolic.
</p>projecteuclid.org/euclid.kjm/1520240411_20180305040022Mon, 05 Mar 2018 04:00 ESTRelative trace formulas for unitary hyperbolic spaceshttps://projecteuclid.org/euclid.kjm/1521856811<strong>Masao Tsuzuki</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 2, 427--491.</p><p><strong>Abstract:</strong><br/>
We develop relative trace formulas of unitary hyperbolic spaces for split rank $1$ unitary groups over totally real number fields.
</p>projecteuclid.org/euclid.kjm/1521856811_20180508040153Tue, 08 May 2018 04:01 EDTAlgebraic cycles and Todorov surfaceshttps://projecteuclid.org/euclid.kjm/1529481671<strong>Robert Laterveer</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 3, 493--527.</p><p><strong>Abstract:</strong><br/>
Motivated by the Bloch–Beilinson conjectures, Voisin has formulated a conjecture about $0$ -cycles on self-products of surfaces of geometric genus one. We verify Voisin’s conjecture for the family of Todorov surfaces with $K^{2}=2$ and fundamental group $\mathbb{Z}/2\mathbb{Z}$ . As a by-product, we prove that certain Todorov surfaces have finite-dimensional motive.
</p>projecteuclid.org/euclid.kjm/1529481671_20180808220323Wed, 08 Aug 2018 22:03 EDTDivisorial contractions to $cDV$ points with discrepancy greater than $1$https://projecteuclid.org/euclid.kjm/1528790514<strong>Yuki Yamamoto</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 3, 529--567.</p><p><strong>Abstract:</strong><br/>
We study $3$ -dimensional divisorial contractions to $cDV$ points with discrepancy greater than $1$ which are of exceptional type. We show that every $3$ -dimensional divisorial contraction is obtained as a weighted blowup.
</p>projecteuclid.org/euclid.kjm/1528790514_20180808220323Wed, 08 Aug 2018 22:03 EDTAmenable absorption in amalgamated free product von Neumann algebrashttps://projecteuclid.org/euclid.kjm/1528185692<strong>Rémi Boutonnet</strong>, <strong>Cyril Houdayer</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 3, 583--593.</p><p><strong>Abstract:</strong><br/>
We investigate the position of amenable subalgebras in arbitrary amalga- mated free product von Neumann algebras $M=M_{1}\ast_{B}M_{2}$ . Our main result states that, under natural analytic assumptions, any amenable subalgebra of $M$ that has a large intersection with $M_{1}$ is actually contained in $M_{1}$ . The proof does not rely on Popa’s asymptotic orthogonality property but on the study of nonnormal conditional expectations.
</p>projecteuclid.org/euclid.kjm/1528185692_20180808220323Wed, 08 Aug 2018 22:03 EDTBayer–Macrì decomposition on Bridgeland moduli spaces over surfaceshttps://projecteuclid.org/euclid.kjm/1529481669<strong>Wanmin Liu</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 3, 595--621.</p><p><strong>Abstract:</strong><br/>
We find a decomposition formula of the local Bayer–Macrì map for the nef line bundle theory on the Bridgeland moduli space over a surface. If there is a global Bayer–Macrì map, then such a decomposition gives a precise correspondence from Bridgeland walls to Mori walls. As an application, we compute the nef cone of the Hilbert scheme $S^{[n]}$ of $n$ -points over special kinds of a fibered surface $S$ of Picard rank $2$ .
</p>projecteuclid.org/euclid.kjm/1529481669_20180808220323Wed, 08 Aug 2018 22:03 EDTLocal Jacquet–Langlands correspondences for simple supercuspidal representationshttps://projecteuclid.org/euclid.kjm/1529373740<strong>Naoki Imai</strong>, <strong>Takahiro Tsushima</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 3, 623--638.</p><p><strong>Abstract:</strong><br/>
We give a description of the local Jacquet–Langlands correspondence for simple supercuspidal representations via type theory. As a consequence, we show that the endoclasses for such representations are invariant under the local Jacquet–Langlands correspondence.
</p>projecteuclid.org/euclid.kjm/1529373740_20180808220323Wed, 08 Aug 2018 22:03 EDTHomological dimensions of rigid moduleshttps://projecteuclid.org/euclid.kjm/1529373739<strong>Majid Rahro Zargar</strong>, <strong>Olgur Celikbas</strong>, <strong>Mohsen Gheibi</strong>, <strong>Arash Sadeghi</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 3, 639--669.</p><p><strong>Abstract:</strong><br/>
We obtain various characterizations of commutative Noetherian local rings $(R,\mathfrak{m})$ in terms of homological dimensions of certain finitely generated modules. Our argument has a series of consequences in different directions. For example, we establish that $R$ is Gorenstein if the Gorenstein injective dimension of the maximal ideal $\mathfrak{m}$ of $R$ is finite. Moreover, we prove that $R$ must be regular if a single $\operatorname{\mathsf{Ext}}_{R}^{n}(I,J)$ vanishes for some integrally closed $\mathfrak{m}$ -primary ideals $I$ and $J$ of $R$ and for some positive integer $n$ .
</p>projecteuclid.org/euclid.kjm/1529373739_20180808220323Wed, 08 Aug 2018 22:03 EDTOn the Galois structure of arithmetic cohomology, III: Selmer groups of critical motiveshttps://projecteuclid.org/euclid.kjm/1529978537<strong>David Burns</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 3, 671--693.</p><p><strong>Abstract:</strong><br/>
We investigate the explicit Galois structures of Bloch–Kato Selmer groups of $p$ -adic realizations of critical motives. We show in particular that, under natural and relatively mild hypotheses, the Krull–Schmidt decompositions of the $p$ -adic lattices arising from such Selmer groups are dominated by very simple indecomposable modules (even when the ranks are very large).
</p>projecteuclid.org/euclid.kjm/1529978537_20180808220323Wed, 08 Aug 2018 22:03 EDTA Fock sheaf for Givental quantizationhttps://projecteuclid.org/euclid.kjm/1532656825<strong>Tom Coates</strong>, <strong>Hiroshi Iritani</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 4, 695--864.</p><p><strong>Abstract:</strong><br/>
We give a global, intrinsic, and coordinate-free quantization formalism for Gromov–Witten invariants and their B-model counterparts, which simultaneously generalizes the quantization formalisms described by Witten, Givental, and Aganagic–Bouchard–Klemm. Descendant potentials live in a Fock sheaf, consisting of local functions on Givental’s Lagrangian cone that satisfy the $(3g-2)$ -jet condition of Eguchi–Xiong; they also satisfy a certain anomaly equation, which generalizes the holomorphic anomaly equation of Bershadsky–Cecotti–Ooguri–Vafa. We interpret Givental’s formula for the higher-genus potentials associated to a semisimple Frobenius manifold in this setting, showing that, in the semisimple case, there is a canonical global section of the Fock sheaf. This canonical section automatically has certain modularity properties. When $X$ is a variety with semisimple quantum cohomology, a theorem of Teleman implies that the canonical section coincides with the geometric descendant potential defined by Gromov–Witten invariants of $X$ . We use our formalism to prove a higher-genus version of Ruan’s crepant transformation conjecture for compact toric orbifolds. When combined with our earlier joint work with Jiang, this shows that the total descendant potential for a compact toric orbifold $X$ is a modular function for a certain group of autoequivalences of the derived category of $X$ .
</p>projecteuclid.org/euclid.kjm/1532656825_20181120220053Tue, 20 Nov 2018 22:00 ESTModuli spaces of stable sheaves on Enriques surfaceshttps://projecteuclid.org/euclid.kjm/1532138461<strong>Kōta Yoshioka</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 4, 865--914.</p><p><strong>Abstract:</strong><br/>
We study the existence condition of $\mu$ -stable sheaves on Enriques surfaces. We also give a different proof of the irreducibility of the moduli spaces of rank 2 stable sheaves.
</p>projecteuclid.org/euclid.kjm/1532138461_20181120220053Tue, 20 Nov 2018 22:00 ESTThe Daugavet equation in Banach spaces with alternatively convex-smooth dualshttps://projecteuclid.org/euclid.kjm/1529481670<strong>Paweł Wójcik</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 58, Number 4, 915--921.</p><p><strong>Abstract:</strong><br/>
This short paper gives a necessary and sufficient condition for the Daugavet equation $\|I+T\|=1+\|T\|$ . A new characterization of the solution of the Daugavet equation in terms of invariant affine subspaces is given. We also study the notions of alternatively convex or smooth ( acs ) and locally uniformly alternatively convex or smooth ( luacs ).
</p>projecteuclid.org/euclid.kjm/1529481670_20181120220053Tue, 20 Nov 2018 22:00 ESTMultiplication of periodic hyperfunctions via harmonic regularization and applicationshttps://projecteuclid.org/euclid.kjm/1546916421<strong>V. Valmorin</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 26 pages.</p><p><strong>Abstract:</strong><br/>
We build a locally convex algebra of real analytic functions defined in a strip of the Poincaré half-plane in which a class of periodic hyperfunctions on the real line is topologically embedded. This is accomplished via a harmonic regularization method. In this algebra, we can give a sense to differential problems involving products of hyperfunctions which are a priori not defined in the classical setting. Some examples and an application are given.
</p>projecteuclid.org/euclid.kjm/1546916421_20190107220044Mon, 07 Jan 2019 22:00 ESTBrane involutions on irreducible holomorphic symplectic manifoldshttps://projecteuclid.org/euclid.kjm/1546916422<strong>Emilio Franco</strong>, <strong>Marcos Jardim</strong>, <strong>Grégoire Menet</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 41 pages.</p><p><strong>Abstract:</strong><br/>
In the context of irreducible holomorphic symplectic manifolds, we say that (anti)holomorphic (anti)symplectic involutions are brane involutions since their fixed point locus is a brane in the physicists’ language, that is, a submanifold which is either a complex or Lagrangian submanifold with respect to each of the three Kähler structures of the associated hyper-Kähler structure. Starting from a brane involution on a $\mathrm{K3}$ or Abelian surface, one can construct a natural brane involution on its moduli space of sheaves. We study these natural involutions and their relation with the Fourier–Mukai transform. Later, we recall the lattice-theoretical approach to mirror symmetry. We provide two ways of obtaining a brane involution on the mirror, and we study the behavior of the brane involutions under both mirror transformations, giving examples in the case of a $\mathrm{K3}$ surface and $\mathrm{K3}^{[2]}$ -type manifolds.
</p>projecteuclid.org/euclid.kjm/1546916422_20190107220044Mon, 07 Jan 2019 22:00 ESTSpecifying the Auslander transpose in submodule category and its applicationshttps://projecteuclid.org/euclid.kjm/1543309295<strong>Abdolnaser Bahlekeh</strong>, <strong>Ali Mahin Fallah</strong>, <strong>Shokrollah Salarian</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 30 pages.</p><p><strong>Abstract:</strong><br/>
Let $(R,\mathfrak{m})$ be a $d$ -dimensional commutative Noetherian local ring. Let $\mathcal{M}$ denote the morphism category of finitely generated $R$ -modules, and let $\mathcal{S}$ be the full subcategory of $\mathcal{M}$ consisting of monomorphisms, known as the submodule category. This article reveals that the Auslander transpose in the category $\mathcal{S}$ can be described explicitly within $\operatorname{mod}R$ , the category of finitely generated $R$ -modules. This result is exploited to study the linkage theory as well as the Auslander–Reiten theory in $\mathcal{S}$ . In addition, motivated by a result of Ringel and Schmidmeier, we show that the Auslander–Reiten translations in the subcategories $\mathcal{H}$ and $\mathcal{G}$ , consisting of all morphisms which are maximal Cohen–Macaulay $R$ -modules and Gorenstein projective morphisms, respectively, may be computed within $\operatorname{mod}R$ via $\mathcal{G}$ -covers. The corresponding result for the subcategory of epimorphisms in $\mathcal{H}$ is also obtained.
</p>projecteuclid.org/euclid.kjm/1543309295_20190107220044Mon, 07 Jan 2019 22:00 ESTBundles of generalized theta functions over abelian surfaceshttps://projecteuclid.org/euclid.kjm/1540001287<strong>Dragos Oprea</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 42 pages.</p><p><strong>Abstract:</strong><br/>
We study the Verlinde bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree $0$ , the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier–Mukai symmetries of the Verlinde bundles are found consistently with strange duality. Along the way, a transformation formula for the theta bundles is derived, extending a theorem of Drézet–Narasimhan from curves to abelian surfaces.
</p>projecteuclid.org/euclid.kjm/1540001287_20190107220044Mon, 07 Jan 2019 22:00 ESTThe balanced tensor product of module categorieshttps://projecteuclid.org/euclid.kjm/1538532153<strong>Christopher L. Douglas</strong>, <strong>Christopher Schommer-Pries</strong>, <strong>Noah Snyder</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 13 pages.</p><p><strong>Abstract:</strong><br/>
The balanced tensor product $M\otimes_{A}N$ of two modules over an algebra $A$ is the vector space corepresenting $A$ -balanced bilinear maps out of the product $M\times N$ . The balanced tensor product ${\mathcal{M}}\boxtimes_{\mathcal{C}}{\mathcal{N}}$ of two module categories over a monoidal linear category ${\mathcal{C}}$ is the linear category corepresenting ${\mathcal{C}}$ -balanced right-exact bilinear functors out of the product category ${\mathcal{M}}\times{\mathcal{N}}$ . We show that the balanced tensor product can be realized as a category of bimodule objects in ${\mathcal{C}}$ , provided the monoidal linear category is finite and rigid.
</p>projecteuclid.org/euclid.kjm/1538532153_20190107220044Mon, 07 Jan 2019 22:00 ESTIndex pairings for $\mathbb{R}^{n}$ -actions and Rieffel deformationshttps://projecteuclid.org/euclid.kjm/1534989636<strong>Andreas Andersson</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 47 pages.</p><p><strong>Abstract:</strong><br/>
With an action $\alpha$ of $\mathbb{R}^{n}$ on a $C^{*}$ -algebra $A$ and a skew-symmetric $n\times n$ matrix $\Theta$ , one can consider the Rieffel deformation $A_{\Theta}$ of $A$ , which is a $C^{*}$ -algebra generated by the $\alpha$ -smooth elements of $A$ with a new multiplication. The purpose of this article is to obtain explicit formulas for $K$ -theoretical quantities defined by elements of $A_{\Theta}$ . We give an explicit realization of the Thom class in $\mathit{KK}$ in any dimension $n$ and use it in the index pairings. For local index formulas we assume that there is a densely defined trace on $A$ , invariant under the action. When $n$ is odd, for example, we give a formula for the index of operators of the form $P\pi^{\Theta}(u)P$ , where $\pi^{\Theta}(u)$ is the operator of left Rieffel multiplication by an invertible element $u$ over the unitization of $A$ and $P$ is the projection onto the nonnegative eigenspace of a Dirac operator constructed from the action $\alpha$ . The results are new also for the undeformed case $\Theta=0$ . The construction relies on two approaches to Rieffel deformations in addition to Rieffel’s original one: Kasprzak deformation and warped convolution. We end by outlining potential applications in mathematical physics.
</p>projecteuclid.org/euclid.kjm/1534989636_20190107220044Mon, 07 Jan 2019 22:00 ESTCohomology for spatial superproduct systemshttps://projecteuclid.org/euclid.kjm/1534989637<strong>Oliver T. Margetts</strong>, <strong>R. Srinivasan</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 23 pages.</p><p><strong>Abstract:</strong><br/>
We introduce a cohomology theory for spatial superproduct systems and compute the $2$ -cocycles for some basic examples called Clifford superproduct systems , thereby distinguishing them up to isomorphism. This consequently proves that a family of $E_{0}$ -semigroups on type III factors, which we call CAR flows , are noncocycle-conjugate for different ranks. Similar results follow for the even CAR flows as well. We also compute the automorphism group of the Clifford superproduct systems.
</p>projecteuclid.org/euclid.kjm/1534989637_20190107220044Mon, 07 Jan 2019 22:00 ESTAffine surfaces with isomorphic $\mathbb{A}^{2}$ -cylindershttps://projecteuclid.org/euclid.kjm/1534838488<strong>Adrien Dubouloz</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 13 pages.</p><p><strong>Abstract:</strong><br/>
We show that all complements of cuspidal hyperplane sections of smooth projective cubic surfaces have isomorphic $\mathbb{A}^{2}$ -cylinders. As a consequence, we derive that the $\mathbb{A}^{2}$ -cancellation problem fails in every dimension greater than or equal to $2$ .
</p>projecteuclid.org/euclid.kjm/1534838488_20190107220044Mon, 07 Jan 2019 22:00 ESTFat-wedge filtration and decomposition of polyhedral productshttps://projecteuclid.org/euclid.kjm/1532743573<strong>Kouyemon Iriye</strong>, <strong>Daisuke Kishimoto</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 51 pages.</p><p><strong>Abstract:</strong><br/>
The polyhedral product constructed from a collection of pairs of cones and their bases and a simplicial complex $K$ is studied by investigating its filtration called the fat-wedge filtration . We give a sufficient condition for decomposing the polyhedral product in terms of the fat-wedge filtration of the real moment-angle complex for $K$ , which is a desuspension of the decomposition of the suspension of the polyhedral product due to Bahri, Bendersky, Cohen, and Gitler. We show that the condition also implies a strong connection with the Golodness of $K$ , and it is satisfied when $K$ is dual sequentially Cohen–Macaulay over $\mathbb{Z}$ or $\lceil\frac{\dim K}{2}\rceil$ -neighborly so that the polyhedral product decomposes. Specializing to the moment-angle complex, we prove that the similar condition on its fat-wedge filtrations is necessary and sufficient for its decomposition.
</p>projecteuclid.org/euclid.kjm/1532743573_20190107220044Mon, 07 Jan 2019 22:00 ESTExtending properties to relatively hyperbolic groupshttps://projecteuclid.org/euclid.kjm/1547802013<strong>Daniel A. Ramras</strong>, <strong>Bobby W. Ramsey</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 14 pages.</p><p><strong>Abstract:</strong><br/>
Consider a finitely generated group $G$ that is relatively hyperbolic with respect to a family of subgroups $H_{1},\ldots,H_{n}$ . We present an axiomatic approach to the problem of extending metric properties from the subgroups $H_{i}$ to the full group $G$ . We use this to show that both (weak) finite decomposition complexity and straight finite decomposition complexity are extendable properties. We also discuss the equivalence of two notions of straight finite decomposition complexity.
</p>projecteuclid.org/euclid.kjm/1547802013_20190118040045Fri, 18 Jan 2019 04:00 ESTTwo applications of strong hyperbolicityhttps://projecteuclid.org/euclid.kjm/1549270868<strong>Bogdan Nica</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 10 pages.</p><p><strong>Abstract:</strong><br/>
We present two analytic applications of the fact that a hyperbolic group can be endowed with a strongly hyperbolic metric. The first application concerns the crossed product $C^{*}$ -algebra defined by the action of a hyperbolic group on its boundary. We construct a natural time flow, involving the Busemann cocycle on the boundary. This flow has a natural KMS state, coming from the Hausdorff measure on the boundary, which is furthermore unique when the group is torsion-free. The second application is a short new proof of the fact that a hyperbolic group admits a proper isometric action on an $\ell ^{p}$ -space for large enough $p$ .
</p>projecteuclid.org/euclid.kjm/1549270868_20190204040138Mon, 04 Feb 2019 04:01 ESTConstructing MASAs with prescribed propertieshttps://projecteuclid.org/euclid.kjm/1551236641<strong>Sorin Popa</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Advance publication, 31 pages.</p><p><strong>Abstract:</strong><br/>
We consider an iterative procedure for constructing maximal abelian $^{*}$ -subalgebras (MASAs) satisfying prescribed properties in II $_{1}$ factors. This method pairs well with the intertwining by bimodules technique and with properties of the MASA and of the ambient factor that can be described locally. We obtain such a local characterization for II $_{1}$ factors $M$ that have an s-MASA , $A\subset M$ (i.e., for which $A\veeJAJ$ is maximal abelian in $\mathcal {B}(L^{2}M)$ ), and use this strategy to prove that any factor in this class has uncountably many nonintertwinable singular (resp., semiregular) s-MASAs.
</p>projecteuclid.org/euclid.kjm/1551236641_20190226220456Tue, 26 Feb 2019 22:04 ESTProjective unitary representations of infinite-dimensional Lie groupshttps://projecteuclid.org/euclid.kjm/1554170605<strong>Bas Janssens</strong>, <strong>Karl-Hermann Neeb</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 293--341.</p><p><strong>Abstract:</strong><br/>
For an infinite-dimensional Lie group $G$ modeled on a locally convex Lie algebra ${\mathfrak{g}}$ , we prove that every smooth projective unitary representation of $G$ corresponds to a smooth linear unitary representation of a Lie group extension $G^{\sharp}$ of $G$ . (The main point is the smooth structure on $G^{\sharp}$ .) For infinite-dimensional Lie groups $G$ which are $1$ -connected, regular, and modeled on a barreled Lie algebra ${\mathfrak{g}}$ , we characterize the unitary ${\mathfrak{g}}$ -representations which integrate to $G$ . Combining these results, we give a precise formulation of the correspondence between smooth projective unitary representations of $G$ , smooth linear unitary representations of $G^{\sharp}$ , and the appropriate unitary representations of its Lie algebra ${\mathfrak{g}}^{\sharp}$ .
</p>projecteuclid.org/euclid.kjm/1554170605_20190527040153Mon, 27 May 2019 04:01 EDTUniform K-stability and plt blowups of log Fano pairshttps://projecteuclid.org/euclid.kjm/1555660964<strong>Kento Fujita</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 399--418.</p><p><strong>Abstract:</strong><br/>
We show relationships between uniform K-stability and plt blowups of log Fano pairs. We see that it is enough to evaluate certain invariants defined by volume functions for all plt blowups in order to test the uniform K-stability of log Fano pairs. We also discuss the uniform K-stability of two log Fano pairs under crepant finite covers. Moreover, we give another proof of the K-semistability of the projective plane.
</p>projecteuclid.org/euclid.kjm/1555660964_20190527040153Mon, 27 May 2019 04:01 EDTOn $n$ -dimensional fractional Hardy operators and commutators in variable Herz-type spaceshttps://projecteuclid.org/euclid.kjm/1555660963<strong>Liwei Wang</strong>, <strong>Meng Qu</strong>, <strong>Wenyu Tao</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 419--439.</p><p><strong>Abstract:</strong><br/>
Based on the theory of variable exponents and atomic decomposition, we study the boundedness of $n$ -dimensional fractional Hardy operators on variable Herz and Herz-type Hardy spaces, where the three main indices are variable exponents. The corresponding boundedness for the $m$ th order commutators generated by the $n$ -dimensional fractional Hardy operators and bounded mean oscillation (BMO) function are also considered. We note that, even in the special case of $m=1$ , the obtained results are also new.
</p>projecteuclid.org/euclid.kjm/1555660963_20190527040153Mon, 27 May 2019 04:01 EDTOn some spectral properties of the weighted $\overline{\partial}$ -Neumann operatorhttps://projecteuclid.org/euclid.kjm/1556330547<strong>Franz Berger</strong>, <strong>Friedrich Haslinger</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 441--453.</p><p><strong>Abstract:</strong><br/>
We study necessary conditions for compactness of the weighted $\overline{\partial}$ -Neumann operator on the space $L^{2}(\mathbb{C}^{n},e^{-\varphi})$ for a plurisubharmonic function $\varphi$ . Under the assumption that the corresponding weighted Bergman space of entire functions has infinite dimension, a weaker result is obtained by simpler methods. Moreover, we investigate (non)compactness of the $\overline{\partial}$ -Neumann operator for decoupled weights, which are of the form $\varphi(z)=\varphi_{1}(z_{1})+\cdots +\varphi_{n}(z_{n})$ . More can be said if every $\Delta\varphi_{j}$ defines a nontrivial doubling measure.
</p>projecteuclid.org/euclid.kjm/1556330547_20190527040153Mon, 27 May 2019 04:01 EDTAngehrn–Siu type effective basepoint freeness for quasi-log canonical pairshttps://projecteuclid.org/euclid.kjm/1557216017<strong>Haidong Liu</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 455--470.</p><p><strong>Abstract:</strong><br/>
We prove Angehrn–Siu type effective freeness and effective point separation for quasi-log canonical pairs. As a natural consequence, we obtain that these two results hold for semi-log canonical pairs. One of the main ingredients of our proof is inversion of adjunction for quasi-log canonical pairs, which is established in this paper.
</p>projecteuclid.org/euclid.kjm/1557216017_20190527040153Mon, 27 May 2019 04:01 EDTThe notion of cusp forms for a class of reductive symmetric spaces of split rank $1$https://projecteuclid.org/euclid.kjm/1557367351<strong>Erik P. van den Ban</strong>, <strong>Job J. Kuit</strong>, <strong>Henrik Schlichtkrull</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 2, 471--513.</p><p><strong>Abstract:</strong><br/>
We study a notion of cusp forms for the symmetric spaces $G/H$ with $G=\mathrm{SL}(n,{\mathbb{R}})$ and $H=\mathrm{S}(\mathrm{GL}(n-1,{\mathbb{R}})\times \mathrm{GL}(1,{\mathbb{R}}))$ . We classify all minimal parabolic subgroups of $G$ for which the associated cuspidal integrals are convergent and discuss the possible definitions of cusp forms. Finally, we show that the closure of the direct sum of the discrete series representations of $G/H$ coincides with the space of cusp forms.
</p>projecteuclid.org/euclid.kjm/1557367351_20190527040153Mon, 27 May 2019 04:01 EDTExplicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaceshttps://projecteuclid.org/euclid.kjm/1563242599<strong>Arata Komyo</strong>, <strong>Masa-Hiko Saito</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 515--552.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the apparent singularities and the dual parameters of rank $2$ parabolic connections on $\mathbb{P}^{1}$ and rank $2$ (parabolic) Higgs bundles on $\mathbb{P}^{1}$ . Then we obtain explicit descriptions of Zariski-open sets of the moduli space of the parabolic connections and the moduli space of the Higgs bundles. For $n=5$ , we can give global descriptions of the moduli spaces in detail.
</p>projecteuclid.org/euclid.kjm/1563242599_20190807040132Wed, 07 Aug 2019 04:01 EDTA fractional calculus approach to rough integrationhttps://projecteuclid.org/euclid.kjm/1558059097<strong>Yu Ito</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 553--573.</p><p><strong>Abstract:</strong><br/>
On the basis of fractional calculus, we introduce an integral of controlled paths against $\beta $ -Hölder rough paths with $\beta \in (1/3,1/2]$ . The integral is defined by the Lebesgue integrals for fractional derivative operators, without using any argument based on discrete approximation. We show in this article that the integral is consistent with that obtained by the usual integration in rough path analysis, given by the limit of the compensated Riemann–Stieltjes sums.
</p>projecteuclid.org/euclid.kjm/1558059097_20190807040132Wed, 07 Aug 2019 04:01 EDTCotorsion pairs in categories of quiver representationshttps://projecteuclid.org/euclid.kjm/1556157622<strong>Henrik Holm</strong>, <strong>Peter Jørgensen</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 575--606.</p><p><strong>Abstract:</strong><br/>
We study the category $\operatorname{Rep}(Q,\mathcal{M})$ of representations of a quiver $Q$ with values in an abelian category $\mathcal{M}$ . Under certain assumptions, we show that every cotorsion pair $(\mathcal{A},\mathcal{B})$ in $\mathcal{M}$ induces two (explicitly described) cotorsion pairs $(\Phi (\mathcal{A}),\operatorname{Rep}(Q,\mathcal{B}))$ and $(\operatorname{Rep}(Q,\mathcal{A}),\Psi (\mathcal{B}))$ in $\operatorname{Rep}(Q,\mathcal{M})$ . This is akin to a result by Gillespie, which asserts that a cotorsion pair $(\mathcal{A},\mathcal{B})$ in $\mathcal{M}$ induces cotorsion pairs $(\widetilde{\mathcal{A}},\operatorname{dg}\widetilde{\mathcal{B}})$ and $(\operatorname{dg}\widetilde{\mathcal{A}},\widetilde{\mathcal{B}})$ in the category $\operatorname{Ch}(\mathcal{M})$ of chain complexes in $\mathcal{M}$ . Special cases of our results recover descriptions of the projective and injective objects in $\operatorname{Rep}(Q,\mathcal{M})$ proved by Enochs, Estrada, and García Rozas.
</p>projecteuclid.org/euclid.kjm/1556157622_20190807040132Wed, 07 Aug 2019 04:01 EDTA local rigidity theorem for finite actions on Lie groups and application to compact extensions of $\mathbb{R}^{n}$https://projecteuclid.org/euclid.kjm/1560218486<strong>Ali Baklouti</strong>, <strong>Souhail Bejar</strong>, <strong>Ramzi Fendri</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 607--618.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a Lie group, and let $\Gamma$ be a finite group. We show in this article that the space $\operatorname{Hom}(\Gamma ,G)/G$ is discrete and—in addition—finite if $G$ has finitely many connected components. This means that in the case in which $\Gamma$ is a discontinuous group for the homogeneous space $G/H$ , where $H$ is a closed subgroup of $G$ , all the elements of Kobayashi’s parameter space are locally rigid. Equivalently, any Clifford–Klein form of finite fundamental group does not admit nontrivial continuous deformations. As an application, we provide a criterion of local rigidity in the context of compact extensions of $\mathbb{R}^{n}$ .
</p>projecteuclid.org/euclid.kjm/1560218486_20190807040132Wed, 07 Aug 2019 04:01 EDTExplicit calculation of local integrals for twisted triple product $L$ -functionshttps://projecteuclid.org/euclid.kjm/1558145160<strong>Isao Ishikawa</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 619--648.</p><p><strong>Abstract:</strong><br/>
Ichino proved a formula expressing global trilinear period integrals as products of central values of triple product $L$ -functions and certain local trilinear integrals. In general, these local trilinear integrals are difficult to evaluate, and the main result in this article is to prove an identity relating local trilinear integrals and products of local Rankin–Selberg integrals in the twisted case. This result has applications to an explicit version of Ichino’s formula and the construction of $p$ -adic $L$ -functions for twisted triple products in our forthcoming works.
</p>projecteuclid.org/euclid.kjm/1558145160_20190807040132Wed, 07 Aug 2019 04:01 EDTSpin networks, Ehrhart quasipolynomials, and combinatorics of dormant indigenous bundleshttps://projecteuclid.org/euclid.kjm/1562032985<strong>Yasuhiro Wakabayashi</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 649--684.</p><p><strong>Abstract:</strong><br/>
It follows from work of S. Mochizuki, F. Liu, and B. Osserman that there is a relationship between Ehrhart’s theory concerning rational polytopes and the geometry of the moduli stack classifying dormant indigenous bundles on a proper hyperbolic curve in positive characteristic. This relationship was established by considering the (finite) cardinality of the set consisting of certain colorings on a $3$ -regular graph called spin networks . In the present article, we recall the correspondences between spin networks, lattice points of rational polytopes, and dormant indigenous bundles and present some identities and explicit computations of invariants associated with the objects involved.
</p>projecteuclid.org/euclid.kjm/1562032985_20190807040132Wed, 07 Aug 2019 04:01 EDTDeformation equivalence classes of Inoue surfaces with $b_{1}=1$ and $b_{2}=0$https://projecteuclid.org/euclid.kjm/1558145161<strong>Shota Murakami</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 685--701.</p><p><strong>Abstract:</strong><br/>
In this article, we will show that if $S$ is an Inoue surface with $b_{1}=1$ and $b_{2}=0$ , then the number of deformation equivalence classes of complex surfaces diffeomorphic to $S$ is at most $16$ .
</p>projecteuclid.org/euclid.kjm/1558145161_20190807040132Wed, 07 Aug 2019 04:01 EDTSmall embeddings of integral domainshttps://projecteuclid.org/euclid.kjm/1558404168<strong>Yu Yang Bao</strong>, <strong>Daniel Daigle</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 703--716.</p><p><strong>Abstract:</strong><br/>
Let $A$ be a geometrically integral algebra over a field $k$ . We prove that, for any affine $k$ -domain $R$ , if there exists an extension field $K$ of $k$ such that $R\subseteq K\otimes_{k}A$ and $R\nsubseteq K$ , then there exists an extension field $L$ of $k$ such that $R\subseteqL\otimes_{k}A$ and $\operatorname{trdeg}_{k}(L)\lt \operatorname{trdeg}_{k}(R)$ . This generalizes a result of Freudenburg, namely, the fact that this is true for $A=k^{[1]}$ .
</p>projecteuclid.org/euclid.kjm/1558404168_20190807040132Wed, 07 Aug 2019 04:01 EDTKolyvagin systems and Iwasawa theory of generalized Heegner cycleshttps://projecteuclid.org/euclid.kjm/1562896995<strong>Matteo Longo</strong>, <strong>Stefano Vigni</strong>. <p><strong>Source: </strong>Kyoto Journal of Mathematics, Volume 59, Number 3, 717--746.</p><p><strong>Abstract:</strong><br/>
Iwasawa theory of Heegner points on abelian varieties of $\operatorname{GL}_{2}$ type has been studied by, among others, Mazur, Perrin-Riou, Bertolini, and Howard. The purpose of this article is to describe extensions of some of their results in which abelian varieties are replaced by the Galois cohomology of Deligne’s $p$ -adic representation attached to a modular form of even weight greater than $2$ . In this setting, the role of Heegner points is played by higher-dimensional Heegner-type cycles that have been recently defined by Bertolini, Darmon, and Prasanna. Our results should be compared with those obtained, via deformation-theoretic techniques, by Fouquet in the context of Hida families of modular forms.
</p>projecteuclid.org/euclid.kjm/1562896995_20190807040132Wed, 07 Aug 2019 04:01 EDT