Approximation of sheaves on algebraic stacks

Abstract

Raynaud--Gruson characterized flat and pure morphisms between affine schemes in terms of projective modules. We give a similar characterization for non-affine morphisms. As an application, we show that every quasi-coherent sheaf is the union of its finitely generated quasi-coherent subsheaves on any quasi-compact and quasi-separated algebraic stack.

17 pages; generalized result to all quasi-compact and quasi-separated algebraic stacks; added some applications; major revision; final version

References in corpus (2)

• Coherent Tannaka duality and algebraicity of Hom-stacks
• Algebraic groups and compact generation of their derived categories of representations

Cited by in corpus (12)

• Coherent Tannaka duality and algebraicity of Hom-stacks
• Algebraic groups and compact generation of their derived categories of representations
• Geometricity for derived categories of algebraic stacks
• The étale local structure of algebraic stacks
• K-theory and G-theory of derived algebraic stacks
• Mayer-Vietoris squares in algebraic geometry
• Resolution and alteration with ample exceptional divisor
• Addendum: Étale dévissage, descent and pushouts of stacks
• A generalization of Luna's fundamental lemma for stacks with good moduli spaces
• The Chabauty-Kim Method for Relative Completions
• Oriented embedding functors of tori as homogeneous spaces
• Drinfeld-Lau Descent over Fibered Categories