Algebra & Number Theory

Semistable periods of finite slope families

Ruochuan Liu

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at msp.org/ant.

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We introduce the notion of finite slope families to encode the local properties of the p-adic families of Galois representations appearing in the work of Harris, Lan, Taylor and Thorne on the construction of Galois representations for (non-self-dual) regular algebraic cuspidal automorphic representations of GL(n) over CM fields. Our main result is to prove the analytic continuation of semistable (and crystalline) periods for such families.

Article information

Source
Algebra Number Theory, Volume 9, Number 2 (2015), 435-458.

Dates
Received: 11 February 2014
Revised: 9 December 2014
Accepted: 14 January 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842286

Digital Object Identifier
doi:10.2140/ant.2015.9.435

Mathematical Reviews number (MathSciNet)
MR3320848

Zentralblatt MATH identifier
06424750

Subjects
Primary: 11F80: Galois representations

Keywords
finite slope families semistable $(\varphi,\Gamma)$-modules

Citation

Liu, Ruochuan. Semistable periods of finite slope families. Algebra Number Theory 9 (2015), no. 2, 435--458. doi:10.2140/ant.2015.9.435. https://projecteuclid.org/euclid.ant/1510842286


Export citation

References

  • Y. André, “Filtrations de type Hasse–Arf et monodromie $p$-adique”, Invent. Math. 148:2 (2002), 285–317.
  • J. Bellaïche and G. Chenevier, Families of Galois representations and Selmer groups, Astérisque 324, 2009.
  • R. Bellovin, “$p$-adic Hodge theory in rigid analytic families”, Algebra Number Theory 9:2 (2015), 371–433.
  • L. Berger, “Représentations $p$-adiques et équations différentielles”, Invent. Math. 148:2 (2002), 219–284.
  • L. Berger, “Construction de $(\phi,\Gamma)$-modules: représentations $p$-adiques et $B$-paires”, Algebra Number Theory 2:1 (2008), 91–120.
  • L. Berger, “Équations différentielles $p$-adiques et $(\phi,N)$-modules filtrés”, pp. 13–38 in Représentations $p$-adiques de groupes $p$-adiques, I: Représentations galoisiennes et $(\phi,\Gamma)$-modules, edited by L. Berger et al., Astérisque 319, 2008.
  • L. Berger and P. Colmez, “Familles de représentations de de Rham et monodromie $p$-adique”, pp. 303–337 in Représentations $p$-adiques de groupes $p$-adiques, I: Représentations galoisiennes et $(\phi,\Gamma)$-modules, edited by L. Berger et al., Astérisque 319, 2008.
  • M. Harris, K.-W. Lan, R. Taylor, and J. Thorne, “On the rigid cohomology of certain Shimura varieties”, preprint, 2014.
  • K. Kedlaya and R. Liu, “On families of ($\phi$, $\Gamma$)-modules”, Algebra Number Theory 4:7 (2010), 943–967.
  • K. S. Kedlaya, J. Pottharst, and L. Xiao, “Cohomology of arithmetic families of $(\varphi,\Gamma)$-modules”, J. Amer. Math. Soc. 27:4 (2014), 1043–1115.
  • M. Kisin, “Overconvergent modular forms and the Fontaine–Mazur conjecture”, Invent. Math. 153:2 (2003), 373–454.
  • R. Liu, “Triangulation of refined families”, preprint, 2014.
  • Z. Mebkhout, “Analogue $p$-adique du théorème de Turrittin et le théorème de la monodromie $p$-adique”, Invent. Math. 148:2 (2002), 319–351.
  • S. Shah, “Interpolating periods”, preprint, 2013.
  • C. Skinner and E. Urban, “Vanishing of $L$-functions and ranks of Selmer groups”, pp. 473–500 in International Congress of Mathematicians, Volume II, edited by M. Sanz-Solé et al., Eur. Math. Soc., Zürich, 2006.
  • J. T. Tate, “$p$-divisible groups”, pp. 158–183 in Proceedings of a Conference on Local Fields (Driebergen, 1966), edited by T. Springer, Springer, Berlin, 1967.