| | |
Summary: J. ALGEBRAIC GEOMETRY
00 (XXXX) 000{000
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 nitely
generated p torsion module M over the Iwasawa algebra G of G in
terms of twisted invariants of M , which are de ned 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 nitely 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 nitely generated p torsion module has integral Euler char-
acteristic. Under a slightly weaker condition on G we decompose the
completed group
algebra
|
