Seminar

We will describe how the crystalline cohomology of a supersingular K3 surface gives rise to certain one-parameter families of K3 surfaces, which we call supersingular twistor spaces. Our construction relies on the special behavior of p-torsion classes in the Brauer group of a supersingular K3 surface, as well as techniques coming from the study of derived categories and Fourier-Mukai equivalences. As an application, we will describe a new proof of Ogus's crystalline Torelli theorem, which we extend to small characteristic.