A Derived Gabriel–Popescu Theorem for t-Structures via Derived Injectives. (28th January 2022)

• Record Type: Journal Article
• Authors: Genovese, Francesco; Ramos González, Julia
• Is Part Of: International mathematics research notices. Volume 2023:Number 6(2023)
• Page Start: 4695
• Page End: 4760
• Publication Date: 2022-01-28
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnab367
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: We prove a derived version of the Gabriel–Popescu theorem in the framework of dg-categories and t-structures. This exhibits any pretriangulated dg-category with a suitable t-structure (such that its heart is a Grothendieck abelian category) as a t-exact localization of a derived dg-category of dg-modules. We give an original proof based on a generalization of Mitchell's argument in A quick proof of the Gabriel-Popesco theorem that involves derived injective objects. As an application, we provide a short proof of the fact that derived categories of Grothendieck abelian categories have a unique dg-enhancement.