Derived isogenies between abelian varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915693190971392 |
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| author | Li, Zhiyuan Lu, Ziwei Tang, Zhichao |
| author_facet | Li, Zhiyuan Lu, Ziwei Tang, Zhichao |
| contents | In this paper, we establish a derived Torelli Theorem for twisted abelian varieties. Starting from this, we explore the relation between derived isogenies and classical isogenies. We show that two abelian varieties of dimension $\geq 2$ are derived isogenous if and only if they are principally isogenous over fields of characteristic zero. This generalized the result for abelian surfaces and completely solves the question raised in [arXiv:2108.08710]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derived isogenies between abelian varieties Li, Zhiyuan Lu, Ziwei Tang, Zhichao Algebraic Geometry In this paper, we establish a derived Torelli Theorem for twisted abelian varieties. Starting from this, we explore the relation between derived isogenies and classical isogenies. We show that two abelian varieties of dimension $\geq 2$ are derived isogenous if and only if they are principally isogenous over fields of characteristic zero. This generalized the result for abelian surfaces and completely solves the question raised in [arXiv:2108.08710]. |
| title | Derived isogenies between abelian varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2510.22612 |