Picard groups in $p$-adic Fourier theory

TL;DR

This paper investigates the structure of the Picard and Grothendieck groups of a rigid analytic variety parametrizing locally analytic characters of the integers in a p-adic field extension, contributing to p-adic Fourier theory.

Contribution

It provides new insights into the Picard and Grothendieck groups of character varieties in p-adic Fourier analysis, extending previous work on vector bundles over these varieties.

Findings

Determined the Picard group structure of the character variety.

Analyzed the Grothendieck group in the p-adic setting.

Replaced earlier preprint with a finalized version in Manuscripta Mathematica.

Abstract

Let $L$ be a proper finite extension of the field of $p$-adic numbers and let $o\subset L$ be its integers, viewed as an abelian locally $L$-analytic group. Let $\hat{o}$ be the rigid analytic group variety parametrizing the locally analytic characters of o. We study the Picard group and the Grothendieck group of this variety. This preprint is in final version, replaces the former preprint 'Vector bundles over analytic character varieties' and appears in Manuscripta Mathematica.