Derived isogenies between abelian varieties

2025/10/26 by Li, Zhiyuan, Lu, Ziwei, Tang, Zhichao
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.22612

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 ≥ 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].

Citations

• Point Objects and Derived Equivalences of Twisted Derived Categories of Abelian Varieties
• Semi-Homogeneous Sheaves and Twisted Derived Categories
• Derived isogenies and isogenies for abelian surfaces
• On equivariant triangulated categories
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• Twisted automorphisms of group algebras
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Related

• Derived isogenies and isogenies for abelian surfaces
• Isogenies of abelian varieties over finite fields
• L-series and isogenies of abelian varieties
• Classe d'isogénie de variétés abéliennes pleinement de type GSp
• Essential dimension of isogenies