A tropical formula for non-Archimedean local heights
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909949397827584 |
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| author | Gil, José Ignacio Burgos Gubler, Walter Künnemann, Klaus |
| author_facet | Gil, José Ignacio Burgos Gubler, Walter Künnemann, Klaus |
| contents | We introduce delta-forms on tropical toric varieties generalizing the construction of Mihatsch for $R^n$. These delta-forms will be used to define the star-product with Green functions of piecewise smooth type on a tropical toric variety. As an application, we show that non-archimedean local heights of projective varieties can be computed using the star-product on a suitable complete tropical toric variety.
On the way, we show that open subsets of a simplicial tropical toric variety have a locally finite simplicial decomposition which is constant towards the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A tropical formula for non-Archimedean local heights Gil, José Ignacio Burgos Gubler, Walter Künnemann, Klaus Algebraic Geometry Number Theory Primary 14G40, Secondary 14M25, 14T25, 32P05, 32U40, 52B20 We introduce delta-forms on tropical toric varieties generalizing the construction of Mihatsch for $R^n$. These delta-forms will be used to define the star-product with Green functions of piecewise smooth type on a tropical toric variety. As an application, we show that non-archimedean local heights of projective varieties can be computed using the star-product on a suitable complete tropical toric variety. On the way, we show that open subsets of a simplicial tropical toric variety have a locally finite simplicial decomposition which is constant towards the boundary. |
| title | A tropical formula for non-Archimedean local heights |
| topic | Algebraic Geometry Number Theory Primary 14G40, Secondary 14M25, 14T25, 32P05, 32U40, 52B20 |
| url | https://arxiv.org/abs/2512.07431 |