 
Summary: J. ALGEBRAIC GEOMETRY
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CHARACTERISTIC ELEMENTS FOR pTORSION
IWASAWA MODULES
KONSTANTIN ARDAKOV AND SIMON WADSLEY
Abstract
Let G be a compact padic analytic group with no elements of order p.
We provide a formula for the characteristic element [3] of any finitely
generated ptorsion module M over the Iwasawa algebra G of G in
terms of twisted µinvariants 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 pseudonull ptorsion
module has trivial characteristic element as the pnilpotent groups. It
is also shown that these are precisely the groups which have the property
that every finitely generated ptorsion 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
