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arXiv · 2510.22612

Derived isogenies between abelian varieties

Zhiyuan Li·Ziwei Lu·Zhichao Tang
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Abstract

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].

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Zhiyuan Li, Ziwei Lu, Zhichao Tang. 2025-10-26. Derived isogenies between abelian varieties. https://arxiv.org/abs/2510.22612

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