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Abstract
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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.
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Keywords
Selmer group, noncommutative Iwasawa theory
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Mathematical Subject Classification 2010
Primary: 11R23
Secondary: 16S50
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Milestones
Received: 21 October 2015
Revised: 22 December 2015
Accepted: 1 February 2016
Published: 12 June 2016
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