On twists of modules over noncommutative Iwasawa algebras

Jha, S. and Ochiai, T. and Zábrádi, Gergely (2016) On twists of modules over noncommutative Iwasawa algebras. ALGEBRA AND NUMBER THEORY, 10 (3). pp. 685-694. ISSN 1937-0652

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Abstract

It is well known that, for any finitely generated torsion module M over the Iwasawa algebra ℤp[[Γ]], where Γ is isomorphic to ℤp, there exists a continuous pp-adic character p of Γ such that, for every open subgroup U of Γ, the group of U-coinvariants M(p)U is finite; here M(p) denotes the twist of M by pp. This twisting lemma was already used to study various arithmetic properties of Selmer groups and Galois cohomologies over a cyclotomic tower by Greenberg and Perrin-Riou. We prove a noncommutative generalization of this twisting lemma, replacing torsion modules over ℤp[[Γ]] by certain torsion modules over ℤp[[G]] with more general p-adic Lie group G. In a forthcoming article, this noncommutative twisting lemma will be used to prove the functional equation of Selmer groups of general pp-adic representations over certain p-adic Lie extensions.

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