Automatic meromorphy in non-archimedean geometry

2024/07/30 by Ducros, Antoine
#14G22 #14G99 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.20915

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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