Lifting derived equivalences of abelian surfaces to generalized Kummer varieties · arXivDesk
2507.11358Jul 15, 2025Based on the mistake on previous Lemma 1.4 (It is deleted now.), the contents of Proposition 1.26, Proposition 1.29 and Lemma 1.30 are slightly different. Also, Corollary 0.4 and subsection 2.3 are added to emphasize the finite index property of the lifting results
Lifting derived equivalences of abelian surfaces to generalized Kummer varieties
In this article, we study the G-autoequivalences of the derived category DGb(A) of G-equivariant objects for an abelian variety A with G
Nearby in the stack
being a finite subgroup of
Pic0(A)
. We provide a result analogue to Orlov's short exact sequence for derived equivalences of abelian varieties. It can be generalized to the derived equivalences of abelian varieties for a same
G
in general. Furthermore, we find derived equivalences of generalized Kummer varieties by lifting derived equivalences of abelian surfaces using the
G
-equivariant version of Orlov's short exact sequence and some ``splitting" propositions.