Supersingular twistor spaces 
-- Daniel Bragg, April 27, 2018

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We will describe how the crystalline cohomology of a supersingular K3 surface gives rise to certain one-parameter families, which we call supersingular twistor spaces. Our construction relies on the unique behavior of the Brauer group of a supersingular K3 surface, as well as techniques coming from the study of the derived category and Fourier-Mukai equivalences. As applications, we find new proofs of Ogus's crystalline Torelli theorem and Artin's conjecture that supersingular K3 surfaces are unirational. These results are new in small characteristic. This is joint work with Max Lieblich.