Abstract
It is well known that, for any finitely generated torsion module over the Iwasawa algebra , where is isomorphic to , there exists a continuous -adic character of such that, for every open subgroup of , the group of -coinvariants is finite; here denotes the twist of by . 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 by certain torsion modules over with more general -adic Lie group . In a forthcoming article, this noncommutative twisting lemma will be used to prove the functional equation of Selmer groups of general -adic representations over certain -adic Lie extensions.
Citation
Somnath Jha. Tadashi Ochiai. Gergely Zábrádi. "On twists of modules over noncommutative Iwasawa algebras." Algebra Number Theory 10 (3) 685 - 694, 2016. https://doi.org/10.2140/ant.2016.10.685
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