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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.