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arXiv · 1803.07345

A generalization of a theorem of Swan with applications to Iwasawa theory

Andreas Nickel
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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 prove 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.

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Andreas Nickel. 2018-03-20. A generalization of a theorem of Swan with applications to Iwasawa theory. https://arxiv.org/abs/1803.07345

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