Geodesic
On Zhang's Semipositive Metrics
Documenta mathematica, Tome 24 (2019), pp. 331-372
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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 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.
DOI : 10.4171/dm/683
Classification : 14G22, 14G40
Mots-clés : Arakelov geometry, non-Archimedean geometry, model metrics, plurisubharmonic model functions, divisorial points 
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     author = {Walter Gubler and Florent Martin},
     title = {On {Zhang's} {Semipositive} {Metrics}},
     journal = {Documenta mathematica},
     pages = {331--372},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/683},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/683/}
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Walter Gubler; Florent Martin. On Zhang's Semipositive Metrics. Documenta mathematica, Tome 24 (2019), pp. 331-372. doi: 10.4171/dm/683

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