arXiv subjects
Publications and source records attributed to Tyler Lane.
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.
We produce twisted derived equivalences between torsors under abelian varieties and their moduli spaces of simple semi-homogeneous sheaves. We also establish the natural converse to this result and show that a large class of twisted derived equivalences, including all derived equivalences, between torsors arise in this way. As corollaries, we obtain partial extensions of the usual derived equivalence criterion for abelian varieties established by Orlov and Polishchuk.