Appears in collection : A conference in honor of Arthur Ogus on the occasion of his 70th birthday

Classical Torelli theorems are in their very formulation restricted to complex algebraic varieties. In this talk I will discuss a Torelli-type theorem for K3 surfaces in positive characteristic using the derived category of coherent sheaves as a substitute for the integral structure on Betti cohomology. I will also discuss various arithmetic consequences. This is joint work with Max Lieblich.