Daniel Bragg : Twistor spaces for supersingular K3 surfaces

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

Oct. 10, 2018, 4 p.m.

In

427 SEO

Abstract

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 applications, we find new proofs of Ogus's crystalline Torelli theorem and Artin's conjecture on the unirationality of supersingular K3 surfaces. These results are new in small characteristic.