Journal
JOURNAL OF ALGEBRAIC GEOMETRY
Volume 25, Issue 1, Pages 77-139Publisher
UNIV PRESS INC
DOI: 10.1090/jag/656
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Funding
- ANR-grant BERKO
- ERC-Starting grant Nonarcomp [307856]
- CNRS
- NSF
- IHES
- IMJ
- Ecole Polytechnique
- University of Michigan
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1266207] Funding Source: National Science Foundation
- European Research Council (ERC) [307856] Funding Source: European Research Council (ERC)
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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 scaling, 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, using toroidal techniques.
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