On semipositive piecewise linear functions in non-archimedean analytic geometry

2025/03/07 by Gubler, Walter, Rabinoff, Joseph
#14G40 (Primary) 31C05 #32P05 #32U05 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.05513

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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