The Artin-Tate pairing on the Brauer group of a surface.

Abstract: There is a canonical pairing on the Brauer group of a surface over a finite field, and an old conjecture of Tate predicts that this pairing is alternating. I will present a resolution to Tate’s conjecture, whose key ingredient is a circle of ideas originating in algebraic topology, centered around the Steenrod operations. (The talk will assume minimal background in algebraic topology.)