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Article Dans Une Revue Journal of Algebraic Geometry Année : 2015

Singular semipositive metrics in non-Archimedean geometry

S. Boucksom
Charles Favre
  • Fonction : Auteur
M. Jonsson
  • Fonction : Auteur

Résumé

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or plurisubharmonic) metrics on L, and prove the analogue of the following two basic results in the complex case: the set of semipositive metrics is compact modulo constants, and each semipositive metric is a decreasing limit of smooth semipositive ones. In particular, for continuous metrics our definition agrees with the one by S.-W. Zhang. The proofs use multiplier ideals and the construction of suitable models of X over the valuation ring of K.

Dates et versions

hal-00793193 , version 1 (21-02-2013)

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S. Boucksom, Charles Favre, M. Jonsson. Singular semipositive metrics in non-Archimedean geometry. Journal of Algebraic Geometry, 2015, ⟨10.1090/jag/656⟩. ⟨hal-00793193⟩
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