In 1966, Artin and Tate constructed a canonical pairing on the Brauer group of a surface over a finite field, and onjectured it to be alternating. This duality has analogous incarnations across arithmetic and topology, namely the Cassels-Tate pairing for a Jacobian variety, and the linking form on a 5-manifold. I will explain a proof of the conjecture, which is based on a surprising connection to Steenrod operations.

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