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On the local theory of non-archimedean psh functions

  • Lyuhui Wu
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Abstract

The purposes of this paper are two-folded. First, we define a class of local psh functions on Berkovich spaces, and study their properties. In particular, we show that this class of psh functions is equivalent on the one hand to the one defined by Chambert-Loir--Ducros, and is equivalent on the other hand to the class of global psh functions of Boucksom--Favre--Jonsson on projective varieties satisfying the envelope property. Second, making use of our local theory of non-archimedean psh functions, we prove the envelope conjecture for projective normal varieties over a discretely or trivially valued non-archimedean field of residue characteristic zero.

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Cite

BibTeXRIS
BibTeX
@misc{wu2026local,
  title = {{On the local theory of non-archimedean psh functions}},
  author = {Lyuhui Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27610},
  eprint = {2609.27610},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27610},
}
RIS
TY  - UNPB
TI  - On the local theory of non-archimedean psh functions
AU  - Lyuhui Wu
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27610
UR  - https://arxiv.org/abs/2609.27610
AB  - The purposes of this paper are two-folded. First, we define a class of local psh functions on Berkovich spaces, and study their properties. In particular, we show that this class of psh functions is equivalent on the one hand to the one defined by Chambert-Loir--Ducros, and is equivalent on the other hand to the class of global psh functions of Boucksom--Favre--Jonsson on projective varieties satisfying the envelope property. Second, making use of our local theory of non-archimedean psh functions, we prove the envelope conjecture for projective normal varieties over a discretely or trivially valued non-archimedean field of residue characteristic zero.
ER  -