Brauer groups of abelian varieties over fields of finite characteristic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908670622695424 |
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| author | Grammatica, Livia Skorobogatov, Alexei N. Yang, Yuan |
| author_facet | Grammatica, Livia Skorobogatov, Alexei N. Yang, Yuan |
| contents | We study the Brauer group of an abelian variety A over an algebraically closed field of characteristic p focusing on the p-primary torsion, the key part of which is a certain quasi-algebraic unipotent group U_A. We determine its dimension and obtain a sharp upper bound for its p-exponent. The isogeny class of U_A is classified for abelian varieties A of dimension at most 3. For principally polarised abelian varieties we compute the dimension of the p-torsion subgroup of U_A in terms of the Ekedahl--Oort type of A. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08840 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brauer groups of abelian varieties over fields of finite characteristic Grammatica, Livia Skorobogatov, Alexei N. Yang, Yuan Algebraic Geometry 14F22, 11G10, 14F30 We study the Brauer group of an abelian variety A over an algebraically closed field of characteristic p focusing on the p-primary torsion, the key part of which is a certain quasi-algebraic unipotent group U_A. We determine its dimension and obtain a sharp upper bound for its p-exponent. The isogeny class of U_A is classified for abelian varieties A of dimension at most 3. For principally polarised abelian varieties we compute the dimension of the p-torsion subgroup of U_A in terms of the Ekedahl--Oort type of A. |
| title | Brauer groups of abelian varieties over fields of finite characteristic |
| topic | Algebraic Geometry 14F22, 11G10, 14F30 |
| url | https://arxiv.org/abs/2511.08840 |