Student Arithmetic Geometry Seminar: Brauer spaces of spectral algebraic stacks

Seminar | February 14 | 4:10-5 p.m. | 891 Evans Hall

 Chang-Yeon Chough, IBS Center for Geometry and Physics

 Department of Mathematics

Grothendieck posed a question of whether the natural map from the Brauer group of a scheme to its cohomological one is an isomorphism of abelian groups. It's not true in general, but we have some positive results from Grothendieck and Gabber (and de Jong), among many others. After a brief review of Brauer groups in algebraic geometry, I'll talk about some recent progress in the setting of derived and spectral algebraic geometry, where we can provide an affirmative answer for quasi-compact and quasi-separated (derived/spectral) schemes, and my work which extends the previous results to spectral algebraic stacks.