Twisted Derived Equivalences Between Abelian Varieties
Algebraic Geometry
2026-01-26 v1
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.
Keywords
Cite
@article{arxiv.2601.16871,
title = {Twisted Derived Equivalences Between Abelian Varieties},
author = {Tyler Lane},
journal= {arXiv preprint arXiv:2601.16871},
year = {2026}
}
Comments
15 pages