Compact Generation of the Category of D-Modules on the Stack of G-Bundles on a Curve

Abstract

The goal of the paper is to show that the (derived) category of D-modules on the stack (Bun_G(X)) is compactly generated. Here X is a smooth complete curve, and G is a reductive group. The problem is that (Bun_G(X)) is not quasi-compact, so the above compact generation is not automatic. The proof is based on the following observation: (Bun_G(X)) can be written as a union of quasi-compact open substacks, which are "co-truncative", i.e., the (j_!) extension functor is defined on the entire category of D-modules.