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arXiv · 2407.20915

Automatic meromorphy in non-archimedean geometry

Antoine Ducros
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Abstract

In this text we prove that if X is a reduced non-archimedean analytic space and f is a analytic function on a dense Zariski-open subspace of X whose zero-locus is closed in X, then f is a meromorphic function on X. As a corollary, we deduce that every invertible analytic function on the analytification of a reduced scheme of finite type over an affinoid algebra is algebraic.

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Antoine Ducros. 2024-07-30. Automatic meromorphy in non-archimedean geometry. https://arxiv.org/abs/2407.20915

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