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J. ALGEBRAIC GEOMETRY 00 (XXXX) 000000
 

Summary: J. ALGEBRAIC GEOMETRY
00 (XXXX) 000000
S 1056-3911(XX)0000-0
CHARACTERISTIC ELEMENTS FOR p-TORSION
IWASAWA MODULES
KONSTANTIN ARDAKOV AND SIMON WADSLEY
Abstract
Let G be a compact p-adic analytic group with no elements of order p.
We provide a formula for the characteristic element [3] of any finitely
generated p-torsion module M over the Iwasawa algebra G of G in
terms of twisted -invariants of M, which are defined using the Euler
characteristics of M and its twists. A version of the Artin formalism is
proved for these characteristic elements. We characterize those groups
having the property that every finitely generated pseudo-null p-torsion
module has trivial characteristic element as the p-nilpotent groups. It
is also shown that these are precisely the groups which have the property
that every finitely generated p-torsion module has integral Euler char-
acteristic. Under a slightly weaker condition on G we decompose the
completed group algebra G of G with coefficients in Fp into blocks and
show that each block is prime; this generalizes a result of Ardakov and

  

Source: Ardakov, Konstantin - School of Mathematical Sciences, University of Nottingham

 

Collections: Mathematics