Lifting derived equivalences of abelian surfaces to generalized Kummer varieties

In this talk, we study the G-autoequivalences of the derived category D_G^b(A) of G-equivariant coherent sheaves for an abelian variety A with G being a finite subgroup of Pic⁰(A). We provide a result analogous to Orlov’s short exact sequence for derived equivalences of abelian varieties. 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. The talk is based on the paper https://arxiv.org/abs/2507.11358.