Summary: CENTRES OF SKEWFIELDS AND COMPLETELY FAITHFUL
Abstract. Let H be a torsionfree compact padic analytic group whose Lie
algebra is split semisimple. We show that the quotient skewfield of fractions of
the Iwasawa algebra #H of H has trivial centre and use this result to classify
the prime cideals in the Iwasawa algebra #G of G := H × Zp . We also show
that a finitely generated torsion #Gmodule having no nonzero pseudonull
submodule is completely faithful if and only if it is has no central torsion. This
has an application to the study of Selmer groups of elliptic curves.
1.1. Iwasawa algebras. Let p be a prime number. In this note we are concerned
with modules over the Iwasawa algebra
#G := lim
N#oGZ p [G/N ]
of a compact padic analytic group G. These groups frequently occur as images
of Galois representations on ppower division points of abelian varieties and act on
various arithmetic objects of interest such as ideal class groups and Selmer groups.
These arithmetic objects then naturally become modules over the associated Iwa