Tropical Weil's reciprocity law and Weil's pairing
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908575972982784 |
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| author | Kalinin, Nikita Magin, Matthew |
| author_facet | Kalinin, Nikita Magin, Matthew |
| contents | The Weil reciprocity law asserts that given two meromorphic functions $f, g$ on a compact complex curve, the product of the values of $f$ over the roots and poles of $g$ is equal to the product of the values of $g$ over the roots and poles of $f$. We state and prove a tropical version of this reciprocity; the tropical ideas lead to yet another transparent ``combinatorial'' proof of the classical Weil reciprocity law. Then, we construct a tropical Weil pairing on the set of divisors of degree zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tropical Weil's reciprocity law and Weil's pairing Kalinin, Nikita Magin, Matthew Number Theory Algebraic Geometry 14T10, 14T20, 54F50, 11A15 The Weil reciprocity law asserts that given two meromorphic functions $f, g$ on a compact complex curve, the product of the values of $f$ over the roots and poles of $g$ is equal to the product of the values of $g$ over the roots and poles of $f$. We state and prove a tropical version of this reciprocity; the tropical ideas lead to yet another transparent ``combinatorial'' proof of the classical Weil reciprocity law. Then, we construct a tropical Weil pairing on the set of divisors of degree zero. |
| title | Tropical Weil's reciprocity law and Weil's pairing |
| topic | Number Theory Algebraic Geometry 14T10, 14T20, 54F50, 11A15 |
| url | https://arxiv.org/abs/2408.06372 |