Siddharth Mathur, Universidad Católica de Chile
Deformation theory studies the variation of geometric data as a variety moves in a family. In this talk, we will introduce some new deformation-theoretic methods and use them to address a question of Grothendieck from the 1960s: how does the Brauer group of a family compare with that of the various thickenings of a special fiber. We will begin by probing a seemingly simpler question concerning the infinitesimal behavior of invertible sheaves and end by using this to answer Grothendieck’s question.
This is joint work with Andrew Kresch.