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Splitting Brauer classes with the universal Albanese

Algebraic Geometry

Speaker: Wei Ho, University of Michigan
Location: 2112 msb
Start time: Wed, Feb 13 2019, 1:10PM

We prove that every Brauer class over a field splits over a torsor under an abelian variety. If the index of the class is not congruent to 2 modulo 4, we show that the Albanese variety of any smooth curve of positive genus that splits the class also splits the class, and there exist many such curves splitting the class. We show that this can be false when the index is congruent to 2 modulo 4, but adding a single genus 1 factor to the Albanese suffices to split the class. This is joint work with Max Lieblich.