Classically psh and pluriharmonic functions on Berkovich spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911158787637248 |
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| author | Gubler, Walter Rabinoff, Joseph |
| author_facet | Gubler, Walter Rabinoff, Joseph |
| contents | First we extend the theory of subharmonic functions on smooth strictly $k$-analytic curves from Thuillier's thesis to the case of possibly singular analytic curves over a non-archimedean field. Classically psh functions are then defined as in complex geometry by using pullbacks to analytic curves (and requiring compatibility with base change). We give various properties of classically psh functions including a local and a global maximum principle. As a consequence, we show that the space of pluriharmonic functions on a quasi-compact Berkovich space is finite dimensional. As a technical tool, we use that a connected Berkovich space is connected by analytic curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classically psh and pluriharmonic functions on Berkovich spaces Gubler, Walter Rabinoff, Joseph Algebraic Geometry Complex Variables Primary 14G40, Secondary 31C05, 32P05, 32U05 First we extend the theory of subharmonic functions on smooth strictly $k$-analytic curves from Thuillier's thesis to the case of possibly singular analytic curves over a non-archimedean field. Classically psh functions are then defined as in complex geometry by using pullbacks to analytic curves (and requiring compatibility with base change). We give various properties of classically psh functions including a local and a global maximum principle. As a consequence, we show that the space of pluriharmonic functions on a quasi-compact Berkovich space is finite dimensional. As a technical tool, we use that a connected Berkovich space is connected by analytic curves. |
| title | Classically psh and pluriharmonic functions on Berkovich spaces |
| topic | Algebraic Geometry Complex Variables Primary 14G40, Secondary 31C05, 32P05, 32U05 |
| url | https://arxiv.org/abs/2506.13548 |