On the Iwasawa theory of p-adic Lie extensions
Number Theory
2007-05-23 v1
Abstract
In this paper the new techniques and results concerning the structure theory of modules over non-commutative Iwasawa algebras are applied to arithmetic: we study Iwasawa modules over p-adic Lie extensions K of number fields k "up to pseudo-isomorphism". In particular, a close relationship is revealed between the Selmer group of abelian varieties, the Galois group of the maximal abelian unramified p-extension of K as well as the Galois group of the maximal abelian outside S unramified p-extension where S is a finite set of certain places of k. Moreover, we determine the Galois module structure of local units and other modules arising from Galois cohomology.
Keywords
Cite
@article{arxiv.math/0106270,
title = {On the Iwasawa theory of p-adic Lie extensions},
author = {Otmar Venjakob},
journal= {arXiv preprint arXiv:math/0106270},
year = {2007}
}