Nondegenerate G-categories are classified entirely in terms of the root datum of the reductive group G.
Compact generation of the category of D-modules on the stack of G-bundles on a curve
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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.
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Classification of nondegenerate $G$-categories (with an appendix written jointly with Germ\'an Stefanich)
Nondegenerate G-categories are classified entirely in terms of the root datum of the reductive group G.