Minseon Shin (UW)

PDL C-38

**Preseminar 2-2:30**

**Title**: The Brauer group and twisted sheaves

**Abstract**: In this talk I will discuss two definitions of the Brauer group, the comparison map between them, and how surjectivity of this map can be rephrased in terms of the existence of certain vector bundles.

**Seminar 2:30-3:30**

**Title**: Infinite rank twisted vector bundles

**Abstract**: The classical Br = Br' problem asks to classify the schemes X for which every torsion class in H_{et}^2(X,G_m) is representable by a (finite-rank) Azumaya algebra on X. In this talk I will discuss recent work (with Aise Johan de Jong and Max Lieblich) showing that, for a large class of schemes X (including those with the resolution property), every (possibly nontorsion) class in H_{et}^2(X,G_m) is representable by a (possibly infinite-rank) Azumaya algebra on X.

The talk will also be available via Zoom: https://washington.zoom.us/j/689897930

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