Sarah Frei (Dartmouth): Relative Severi-Brauer varieties on K3 surfaces

Geometric realizations (as etale projective bundles) of Brauer classes on surfaces have many applications, such as the arithmetic of surfaces over non-closed fields and rationality of fourfolds (even over the complex numbers). In this talk, I will discuss joint work with Jack Petok and Anthony Varilly-Alvarado, in which we consider constructions of these etale projective bundles for Brauer classes on K3 surfaces. This builds on recent results of van Geemen and Kaputska, who show that some 2-torsion Brauer classes on K3 surfaces have realizations as the exceptional locus of a divisorial contraction on a hyperkahler fourfold.