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Global pluripotential theory over a trivially valued field

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arxiv 1801.08229 v4 pith:TPRUFPKZ submitted 2018-01-24 math.AG

Sébastien Boucksom , Mattias Jonsson This is my paper · ORCID
classification math.AG
keywords fieldfunctionsglobalpluripotentialtheorytriviallyvaluedbehavior
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We develop global pluripotential theory in the setting of Berkovich geometry over a trivially valued field. Specifically, we define and study functions and measures of finite energy and the non-Archimedean Monge-Ampere operator on any (possibly reducible) projective variety. We also investigate the topology of the space of valuations of linear growth, and the behavior of psh functions thereon.

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  1. Global pluripotential theory for adelic line bundles

    math.AG 2025-07 conditional novelty 6.0 of 10

    The category of strongly semiample adelic line bundles on a quasi-projective arithmetic variety is equivalent to line bundles on its Berkovich analytification with norm-equivariant continuous semipositive metrics.

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