Vector bundles over analytic character varieties

Details Vector bundles over analytic character varieties Vector bundles over analytic character varieties

2009-03-27

arxiv.org/abs/0903.4917v1

Mathematics

Representation Theory

24 pages

Scientific paper

Let $\Q_p\subseteq L\subseteq K\subseteq\C_p$ be a chain of complete intermediate fields where $\Q_p\subseteq L$ is finite and $K$ discretely valued. Let $Z$ be a one dimensional finitely generated abelian locally $L$-analytic group and let $\hat{Z}_K$ be its rigid $K$-analytic character group. Generalizing work of Lazard we compute the Picard group and the Grothendieck group of $\hat{Z}_K$. If $Z=\ol$, the integers in $L\neq\Q_p$, we find $Pic(\hol_K)=\Z_p$ which answers a question raised by J. Teitelbaum.

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