Ind-abelian categories and quasi-coherent sheaves

Abstract

We study the question when a category of ind-objects is abelian. Our answer allows a further generalization of the notion of weakly Tannakian categories introduced by the author. As an application we show that, under suitable conditions, the category of coherent sheaves on the product of two schemes with the resolution property is given by the Deligne tensor product of the categories of coherent sheaves of the two factors. To do this we prove that the class of quasi-compact and semi-separated schemes with the resolution property is closed under fiber products.

33 pages

References in corpus (3)

• Quasi-coherent sheaves on the moduli stack of formal groups
• A characterization of categories of coherent sheaves of certain algebraic stacks
• The resolution property of algebraic surfaces

Cited by in corpus (9)

• Local duality in algebra and topology
• Which abelian tensor categories are geometric?
• Bicategorical colimits of tensor categories
• Localizations of tensor categories and fiber products of schemes
• What do abelian categories form?
• Descent via Tannaka duality
• Exponentiable Grothendieck categories in flat Algebraic Geometry
• Uniqueness of fiber functors and universal Tannakian categories
• Tensor products of finitely cocomplete and abelian categories