**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.**