Algebraic groups and compact generation of their derived categories of representations

Abstract

Let $k$ be a field. We characterize the group schemes $G$ over $k$, not necessarily affine, such that ${\mathsf{D}}_{\mathrm{qc}}(B_{k}G)$ is compactly generated. We also describe the algebraic stacks that have finite cohomological dimension in terms of their stabilizer groups.

17 pages; generalized Theorems A and C; final version; some minor corrections and updated citations

References in corpus (3)

• Grothendieck Duality for Deligne-Mumford Stacks
• Approximation of sheaves on algebraic stacks
• Anti-affine algebraic groups

Cited by in corpus (18)

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• Perfect complexes on algebraic stacks
• Geometricity for derived categories of algebraic stacks
• The étale local structure of algebraic stacks
• Approximation of sheaves on algebraic stacks
• Conservative descent for semi-orthogonal decompositions
• An improvement on the base-change theorem and the functor $f^{!}$
• K-theory and G-theory of derived algebraic stacks
• The telescope conjecture for algebraic stacks
• Mayer-Vietoris squares in algebraic geometry
• Analytification of mapping stacks
• Addendum: Étale dévissage, descent and pushouts of stacks
• On nilpotent extensions of $\infty$-categories and the cyclotomic trace
• Additive invariants of orbifolds
• A note on Tannakian categories and mixed motives
• Adelic Descent Theory
• Unipotent morphisms
• Scalar extensions of categorical resolutions of singularities