Steenrod operations and symplectic arithmetic duality
Abstract
This expository article elaborates upon my talk at the 2025 AMS Summer Institute on Algebraic Geometry. It gives an introduction to a conjecture from Tate's 1966 S\'eminaire Bourbaki report, predicting the existence of a symplectic form on Brauer groups of surfaces over finite fields, and then an informal tour of the proof in Feng20 and CF.
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