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arXiv · 2601.16871

Twisted Derived Equivalences Between Abelian Varieties

Tyler Lane
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Abstract

We generalize a result of Popa-Schnell and show that the isogeny class of the Picard variety is twisted derived invariant. Using this, we prove that any twisted Fourier-Mukai partner of an abelian variety is an abelian variety. We then provide a necessary and sufficient isogeny-based condition for two abelian varieties to be twisted derived equivalent.

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Tyler Lane. 2026-01-23. Twisted Derived Equivalences Between Abelian Varieties. https://arxiv.org/abs/2601.16871

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