Seminario Teoría de Números UAM-ICMAT

SWAN'S THEOREM AND IWASAWA THEORY

SPEAKER: Andreas Nickel (Universität Duisburg-Essen)

DATE & TIME: MONDAY 25/06/2018, 13:30

PLACE: Aula 420, Departamento de Matemáticas, UAM.

ORGANISER: UAM/ICMAT

ABSTRACT:

Let $p$ be a prime and let $G$ be a finite group. By a celebrated theorem of Swan, two finitely generated projective $mathbb Z_p[G]$-modules $P$ and $P'$ are isomorphic if and only if $mathbb  Q_p otimes_{mathbb Z_p} P$ and $mathbb  Q_p otimes_{mathbb Z_p} P'$ are isomorphic as $mathbb Q_p[G]$-modules.

We discuss an Iwasawa-theoretic analogue of this result and apply this to the Iwasawa theory of local and global fields. We thereby determine the structure of natural Iwasawa modules up to (pseudo-)isomorphism.