On Zhang's Semipositive Metrics

  • Walter Gubler

    Fakultät für Mathematik, Universität Regensburg, Universitätsstrasse 31, D-93040 Regensburg, Germany
  • Florent Martin

    Fakultät für Mathematik, Universität Regensburg, Universitätsstrasse 31, D-93040 Regensburg, Germany
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Abstract

Zhang introduced semipositive metrics on a line bundle of a proper variety. In this paper, we generalize such metrics for a line bundle LL of a paracompact strictly KK-analytic space XX over any non-archimedean field KK. We prove various properties in this setting such as density of piecewise Q\mathbb{Q}-linear metrics in the space of continuous metrics on LL. If XX 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 XX over an arbitrary non-archimedean field KK, the set of semipositive model metrics is closed with respect to pointwise convergence generalizing a result from Boucksom, Favre and Jonsson where KK was assumed to be discretely valued with residue characteristic 00.

Cite this article

Walter Gubler, Florent Martin, On Zhang's Semipositive Metrics. Doc. Math. 24 (2019), pp. 331–372

DOI 10.4171/DM/683