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VOL. 86 | 2020 On spectral sequences for Iwasawa adjoints à la Jannsen for families
Oliver Thomas, Otmar Venjakob

Editor(s) Masato Kurihara, Kenichi Bannai, Tadashi Ochiai, Takeshi Tsuji

Abstract

Jannsen established several spectral sequences for (global and local) Iwasawa modules over (not necessarily commutative) Iwasawa algebras (mainly of $p$-adic Lie groups) over $\mathbb{Z}_p$, which are very useful for determining certain properties of such modules in arithmetic applications. Slight generalizations of said results are also obtained by Nekovář (for abelian groups and more general coefficient rings), by Venjakob (for products of not necessarily abelian groups, but with $\mathbb{Z}_p$-coefficients), and by Lim-Sharifi. Unfortunately, some of Jannsen's spectral sequences for families of representations as coefficients for (local) Iwasawa cohomology are still missing. We explain and follow the philosophy that all these spectral sequences are consequences or analogues of local cohomology and duality à la Grothendieck (and Tate for duality groups).

Information

Published: 1 January 2020
First available in Project Euclid: 12 January 2021

Digital Object Identifier: 10.2969/aspm/08610655

Subjects:
Primary: 11R23 , 13D45

Keywords: and Grothendieck duality , Iwasawa cohomology , Koszul complex , local cohomology , Matlis , Pontrjagin , Tate

Rights: Copyright © 2020 Mathematical Society of Japan

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