Global pluripotential theory for adelic line bundles
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912481848328192 |
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| author | Morrow, Jackson S. |
| author_facet | Morrow, Jackson S. |
| contents | In this work, we relate recent work of Yuan--Zhang and Song on adelic line bundles over quasi-projective arithmetic varieties to recent advances in pluripotential theory on global Berkovich spaces from Pille-Schneider. In particular, we establish an equivalence between subcategories of adelic line bundles on quasi-projective varieties and line bundles on their Berkovich analytifications equipped with a continuous plurisubharmonic metric. We also provide several applications of this equivalence. For example, we generalize a construction of Pille-Schneider concerning families of Monge--Ampère measures on analytifications of projective arithmetic varieties to the quasi-projective setting. With this construction, we offer a new description of non-degenerate subvarieties which involves Monge--Ampère measures over trivially valued fields. Finally, we define a Monge--Ampère measure on the analytification of a quasi-projective arithmetic variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global pluripotential theory for adelic line bundles Morrow, Jackson S. Algebraic Geometry Number Theory In this work, we relate recent work of Yuan--Zhang and Song on adelic line bundles over quasi-projective arithmetic varieties to recent advances in pluripotential theory on global Berkovich spaces from Pille-Schneider. In particular, we establish an equivalence between subcategories of adelic line bundles on quasi-projective varieties and line bundles on their Berkovich analytifications equipped with a continuous plurisubharmonic metric. We also provide several applications of this equivalence. For example, we generalize a construction of Pille-Schneider concerning families of Monge--Ampère measures on analytifications of projective arithmetic varieties to the quasi-projective setting. With this construction, we offer a new description of non-degenerate subvarieties which involves Monge--Ampère measures over trivially valued fields. Finally, we define a Monge--Ampère measure on the analytification of a quasi-projective arithmetic variety. |
| title | Global pluripotential theory for adelic line bundles |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2507.10410 |