Derived categories of torsors for abelian schemes (Q728214)

The authors show that there exist non-isomorphic derived equivalent genus 1 curves; it was previously known that all derived equivalent genus 1 curves \textit{over an algebraically closed field} are isomorphic. More generally, they give necessary and sufficient conditions for the existence of a derived equivalence between torsors over an elliptic curve (Theorem 1.1). The authors obtain additional results concerning derived equivalences of torsors over general abelian varieties (e.g. Theorem 1.4). Along the way, they study derived equivalences of elliptic fibrations, giving a partial answer to a question of Căldăraru (Theorem 1.5).