Compact generation of the category of D-modules on the stack of G-bundles on a curve

Understand

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.