(DOI) 10.1007/s100970100038

** ** pdf-file ** **
auslander.pdf

Abstract: This paper is lead by the question whether there is a nice
structure theory of finitely generated modules over the Iwasawa
algebra, i.e. the completed group algebra, R of a p-adic
analytic group G. For G without any p-torsion element we
prove that R is an Auslander regular ring. This result enables
us to give a good definition for pseudo-null R-modules.
Then the category of R-modules up to pseudo-isomorphisms is
studied and we obtain a weak structure theorem for the
p-primary part of a finitely generated R-module. A local
duality theorem as well as the Auslander-Buchsbaum equality are
further main issues. The arithmetic applications to the Iwasawa
theory of abelian varieties are published in a forthcoming paper. |