On semipositive piecewise linear functions in non-archimedean analytic geometry

Walter Gubler; Joseph Rabinoff

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arXiv · 2503.05513

On semipositive piecewise linear functions in non-archimedean analytic geometry

Walter Gubler·Joseph Rabinoff

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Abstract

In this paper, we generalize results on Zhang's semipositive model metrics from the algebraic setting to strictly analytic spaces over a non-trivially valued non-Archimedean field. We prove stability under pointwise limits and under forming the maximum. We also prove the maximum principle. As tools, we use a local lifting theorem from the special fiber to the generic fiber of a model and an affinoid Bieri--Groves theorem.

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BibTeX RIS

Walter Gubler, Joseph Rabinoff. 2025-03-07. On semipositive piecewise linear functions in non-archimedean analytic geometry. https://arxiv.org/abs/2503.05513

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