## Arithmetic Geometry and Number Theory RTG Seminar: Supersingular twistor space

Seminar | September 17 | 3:10-5 p.m. | 784 Evans Hall

Daniel Bragg, UC Berkeley

Department of Mathematics

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.

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