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Summary: Krull dimension of Iwasawa algebras
and some related topics.
Konstantin Ardakov,
Christ's College.
A dissertation submitted for the degree of
Doctor of Philosophy at the University of Cambridge.
March, 2004.
Abstract
Let G be a uniform pro-p group. We study certain algebraic properties of
the completed group algebra G = Z p [[G]] of G and of other related rings.
First, we consider the Krull dimension K(G ) of G . We establish upper
and lower bounds on K(G ) in terms of the Q p -Lie algebra L(G) of G. We
show these bounds coincide in certain cases, including when L(G) is solvable,
and equal dimG + 1. We also show that K(G ) < dimG + 1 when L(G)
is split simple over Q p . This answers a question of Brown, Hajarnavis and
McEacharn.
Next we study 1-critical modules over the F p -version of Iwasawa algebras,
G = F p [[G]]. We show that the endomorphism ring of such a module M is
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