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arXiv · 2105.02998

Abelian varieties not isogenous to Jacobians over global fields

Ananth N. Shankar·Jacob Tsimerman
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Abstract

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.

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Ananth N. Shankar, Jacob Tsimerman. 2021-05-06. Abelian varieties not isogenous to Jacobians over global fields. https://arxiv.org/abs/2105.02998

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