Geodesic
On Zhang's Semipositive Metrics
Documenta mathematica, Tome 24 (2019), pp. 331-372.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Zhang introduced semipositive metrics on a line bundle of a proper variety. In this paper, we generalize such metrics for a line bundle $L$ of a paracompact strictly $K$-analytic space $X$ over any non-archimedean field $K$. We prove various properties in this setting such as density of piecewise $\mathbb{Q}$-linear metrics in the space of continuous metrics on $L$. If $X$ is proper scheme, then we show that algebraic, formal and piecewise linear metrics are the same. Our main result is that on a proper scheme $X$ over an arbitrary non-archimedean field $K$, the set of semipositive model metrics is closed with respect to pointwise convergence generalizing a result from Boucksom, Favre and Jonsson where $K$ was assumed to be discretely valued with residue characteristic $0$.
Classification : 14G40, 14G22
Keywords: Arakelov geometry, non-Archimedean geometry, model metrics, plurisubharmonic model functions, divisorial points 
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     author = {Gubler, Walter and Martin, Florent},
     title = {On {Zhang's} {Semipositive} {Metrics}},
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Gubler, Walter; Martin, Florent. On Zhang's Semipositive Metrics. Documenta mathematica, Tome 24 (2019), pp. 331-372. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a52/