Formal GAGA for Brauer classes

The relationship between analytic and algebraic geometry (GAGA) is a rich area of study. For example, Grothendieck's existence theorem states that if X is proper over a complete local Noetherian ring A, then a compatible system of coherent sheaves on the thickenings X_n of the special fiber is algebraizable. Such GAGA-type results are now standard tools for studying varieties and their families. In this talk, we answer a question of Grothendieck posed in the 1960s: can a Brauer class on X be determined from a compatible system of classes on the X_n's? This is joint work with Andrew Kresch.