Siddharth Mathur (Universidad Católica de Chile)
PDL C-38
Title: The infinitesimal behavior of line bundles and gerbes
Abstract: Deformation theory is the study of how geometric data varies between the total space of a family of varieties and a given special fiber. In this talk, we will introduce new deformation-theoretic methods to analyze how the Brauer group of a family compares with that of the various thickenings of a special fiber, a question posed by Grothendieck in the early 1960s. We will begin by probing a seemingly simpler question concerning the infinitesimal behavior of the Picard group and end by using this to answer to Grothendieck's question. This is joint work with Andrew Kresch.
Abstract: Deformation theory is the study of how geometric data varies between the total space of a family of varieties and a given special fiber. In this talk, we will introduce new deformation-theoretic methods to analyze how the Brauer group of a family compares with that of the various thickenings of a special fiber, a question posed by Grothendieck in the early 1960s. We will begin by probing a seemingly simpler question concerning the infinitesimal behavior of the Picard group and end by using this to answer to Grothendieck's question. This is joint work with Andrew Kresch.