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arXiv · 2105.02561

A derived Gabriel-Popescu theorem for t-structures via derived injectives

Francesco Genovese·Julia Ramos González
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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" and involving derived injective objects. As an application, we also give a short proof that derived categories of Grothendieck abelian categories have a unique dg-enhancement.

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BibTeXRIS

Francesco Genovese, Julia Ramos González. 2021-05-06. A derived Gabriel-Popescu theorem for t-structures via derived injectives. https://doi.org/10.1093/imrn%2Frnab367

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