Derived equivalences of twisted supersingular K3 surfaces

We study the derived categories of twisted supersingular K3 surfaces. We prove a derived crystalline Torelli theorem for twisted supersingular K3 surfaces, characterizing Fourier-Mukai equivalences in terms of the twisted K3 crystals introduced in [2]. This is a positive characteristic analog of the Hodge-theoretic derived Torelli theorem of Orlov [23] and its extension to twisted K3 surfaces by Huybrechts and Stellari [9,10]. We give applications to various questions concerning Fourier-Mukai partners, extending results of Caldararu [5] and Huybrechts and Stellari [9]. We also give an exact formula for the number of twisted Fourier-Mukai partners of a twisted supersingular K3 surface. (c) 2020 Elsevier Inc. All rights reserved.