Presented By: Algebraic Geometry Seminar - Department of Mathematics
Algebraic Geometry Seminar: Dualizability of derived categories of algebraic stacks
Germán Stefanich (Max Planck Institute for Mathematics)
A fundamental result of Neeman states that the derived category of a quasi compact separated scheme X has a property known as compact generation, which allows one to understand D(X) in terms of a simpler subcategory. In the setting of algebraic stacks, the question of compact generation is more subtle: it turns out to fail in some cases, and the precise generality in which it holds is unknown. Recently, there has been increased interest in a weakening of the notion of compact generation known as dualizability, which still allows for many of the same manipulations that compact generation is used for. In this talk I will review this circle of ideas, and explain a result that characterizes those Noetherian algebraic stacks with affine diagonal X for which D(X) is dualizable.