A Derived Gabriel–Popescu Theorem for t-Structures via Derived Injectives
(2022) International Mathematics Research Notices — Vol. 2023, n° 6, p. 4695-4760 (2023)
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- Authors
Ramos González, Julia 
- 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.
- Affiliations
Univerzita Karlova Matematicko-fyzikální fakulta, Katedra Algebry
Citations
Genovese, F., & Ramos González, J. (2022). A Derived Gabriel–Popescu Theorem for t-Structures via Derived Injectives. International Mathematics Research Notices, 2023(6), 4695-4760. https://doi.org/10.1093/imrn/rnab367 (Original work published 2023)