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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2105.02998 |
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| _version_ | 1866917946645807104 |
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| author | Shankar, Ananth N. Tsimerman, Jacob |
| author_facet | Shankar, Ananth N. Tsimerman, Jacob |
| contents | We prove the existence of abelian varieties not isogenous to Jacobians over characterstic $p$ function fields. Our methods involve studying the action of degree $p$ Hecke operators on hypersymmetric points, as well as their effect on the formal neighborhoods using Serre Tate co-ordinates. We moreover use our methods to provide another proof over number fields, as well as proving a version of this result over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_02998 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Abelian varieties not isogenous to Jacobians over global fields Shankar, Ananth N. Tsimerman, Jacob Number Theory We prove the existence of abelian varieties not isogenous to Jacobians over characterstic $p$ function fields. Our methods involve studying the action of degree $p$ Hecke operators on hypersymmetric points, as well as their effect on the formal neighborhoods using Serre Tate co-ordinates. We moreover use our methods to provide another proof over number fields, as well as proving a version of this result over finite fields. |
| title | Abelian varieties not isogenous to Jacobians over global fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2105.02998 |