Abstract
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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