Derived equivalences of twisted supersingular K3 surfaces

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