On the class group of affinoid spaces

Elkedagmar Heinrich

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A curve $X$ over a non-archimedean valued field is with respect to its analytic structure a finite union of affinoid spaces. The main result states that the class group of a one dimensional, connected, regular affinoid space $Y$ is trivial if and only if $Y$ is a subspace of $P^{1}$ . As a consequence, $X$ has locally a trivial class group if and only if the stable reduction of $X$ has only rational components.

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