Derived isogenies between abelian varieties

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].