On semipositive piecewise linear functions in non-archimedean analytic geometry
Algebraic Geometry
2025-03-10 v1 Number Theory
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.
Cite
@article{arxiv.2503.05513,
title = {On semipositive piecewise linear functions in non-archimedean analytic geometry},
author = {Walter Gubler and Joseph Rabinoff},
journal= {arXiv preprint arXiv:2503.05513},
year = {2025}
}
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26 pages