Sur la dualité et la descente d’Iwasawa

Vauclair, David

doi:10.5802/aif.2446

Cited by 7 publications

(1 citation statement)

References 26 publications

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“…However, in order to be able to work with the Λ-dual, they assume that X consists of (finitely generated) projective Λ-modules. In the case of Iwasawa cohomology that we study, the complex T need not be quasiisomorphic to a bounded complex of R[G F,S ]-modules that are projective and finitely generated over R. Moreover, if R is Gorenstein, then R serves as an R-dualizing complex, and our result reduces to a duality with respect to Λ itself, as in the result of Fukaya-Kato. We also note that Vauclair proved a noncommutative duality theorem for induced modules in the case that R = Z p and T is Z p -free, via a rather different method [Vau,Theorem 6.4].…”

Section: Dualitymentioning

confidence: 99%

Nekovár duality over p-adic Lie extensions of global fields

Lim¹,

Sharifi²

2013

Doc. Math.

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Tate duality is a Pontryagin duality between the ith Galois cohomology group of the absolute Galois group of a local field with coefficents in a finite module and the (2 − i)th cohomology group of the Tate twist of the Pontryagin dual of the module. Poitou-Tate duality has a similar formulation, but the duality now takes place between Galois cohomology groups of a global field with restricted ramification and compactly-supported cohomology groups. Nekovář proved analogues of these in which the module in question is a finitely generated module T over a complete commutative local Noetherian ring R with a commuting Galois action, or a bounded complex thereof, and the Pontryagin dual is replaced with the Grothendieck dual T * , which is a bounded complex of the same form. The cochain complexes computing the Galois cohomology groups of T and T * (1) are then Grothendieck dual to each other in the derived category of finitely generated R-modules. Given a p-adic Lie extension of the ground field, we extend these to dualities between Galois cochain complexes of induced modules of T and T * (1) in the derived category of finitely generated modules over the possibly noncommutative Iwasawa algebra with R-coefficients.

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Section: Dualitymentioning

confidence: 99%

Nekovár duality over p-adic Lie extensions of global fields

Lim¹,

Sharifi²

2013

Doc. Math.

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A generalized Iwasawa’s theorem and its application

Lai

Tan

2021

Res Math Sci

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On Iwasawa Theory of Rubin–stark Units and Narrow Class Groups

Mazigh¹

2018

Glasgow Math. J.

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Let K be a totally real number field of degree r. Let K ∞ denote the cyclotomic Z 2 -extension of K and let L ∞ be a finite extension of K ∞ , abelian over K. The goal of this paper is to compare the characteristic ideal of the χ-quotient of the projective limit of the narrow class groups to the χ-quotient of the projective limit of the r-th exterior power of totally positive units modulo a subgroup of Rubin-Stark units, for some Q 2 -irreducible characters χ of Gal(L ∞ /K ∞ ).

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Sur la dualité et la descente d’Iwasawa

Cited by 7 publications

References 26 publications

Nekovár duality over p-adic Lie extensions of global fields

Nekovár duality over p-adic Lie extensions of global fields

A generalized Iwasawa’s theorem and its application

On Iwasawa Theory of Rubin–stark Units and Narrow Class Groups

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