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# Tony Feng : Steenrod operations and the Artin-Tate pairing

In 1966 Artin and Tate constructed a canonical pairing on the Brauer group of a surface over a finite field, and conjectured 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.

**Category**: Number Theory**Duration**: 01:34:43**Date**: September 6, 2019 at 3:10 PM**Views**: 240-
**Tags:**seminar, Number Theory Seminar

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