Polarizations of abelian varieties over finite fields via canonical liftings
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866915174165774336 |
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| author | Bergström, Jonas Karemaker, Valentijn Marseglia, Stefano |
| author_facet | Bergström, Jonas Karemaker, Valentijn Marseglia, Stefano |
| contents | We describe all polarizations for all abelian varieties over a finite field in a fixed isogeny class corresponding to a squarefree Weil polynomial, when one variety in the isogeny class admits a canonical liftings to characteristic zero, i.e., a lifting for which the reduction morphism induces an isomorphism of endomorphism rings. Categorical equivalences between abelian varieties over finite fields and fractional ideals in étale algebras enable us to explicitly compute isomorphism classes of polarized abelian varieties satisfying some mild conditions. We also implement algorithms to perform these computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_05531 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Polarizations of abelian varieties over finite fields via canonical liftings Bergström, Jonas Karemaker, Valentijn Marseglia, Stefano Number Theory Algebraic Geometry 14K15 (Primary) 14G15, 11G10, 11G25, 14-04 (Secondary) We describe all polarizations for all abelian varieties over a finite field in a fixed isogeny class corresponding to a squarefree Weil polynomial, when one variety in the isogeny class admits a canonical liftings to characteristic zero, i.e., a lifting for which the reduction morphism induces an isomorphism of endomorphism rings. Categorical equivalences between abelian varieties over finite fields and fractional ideals in étale algebras enable us to explicitly compute isomorphism classes of polarized abelian varieties satisfying some mild conditions. We also implement algorithms to perform these computations. |
| title | Polarizations of abelian varieties over finite fields via canonical liftings |
| topic | Number Theory Algebraic Geometry 14K15 (Primary) 14G15, 11G10, 11G25, 14-04 (Secondary) |
| url | https://arxiv.org/abs/2101.05531 |