English

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.

Keywords

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}
}

Comments

26 pages

R2 v1 2026-06-28T22:10:53.874Z