T-structures and twisted complexes on derived injectives

Francesco Genovese; Wendy Lowen; Michel Van den Bergh

doi:10.1016/j.aim.2021.107826

T-structures and twisted complexes on derived injectives

Francesco Genovese, Wendy Lowen, Michel Van den Bergh

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In the paper "Deformation theory of abelian categories", the last two authors proved that an abelian category with enough injectives can be reconstructed as the category of finitely presented modules over the category of its injective objects. We show a generalization of this to pretriangulated dg-categories with a left bounded non-degenerate t-structure with enough derived injectives, the latter being derived enhancements of the injective objects in the heart of the t-structure. Such dg-categories (with an additional hypothesis of closure under suitable products) can be completely described in terms of left bounded twisted complexes of their derived injectives.

Original language	English
Article number	107826
Number of pages	70
Journal	Advances in Mathematics
Volume	387
DOIs	https://doi.org/10.1016/j.aim.2021.107826
Publication status	Published - 27 Aug 2021

Bibliographical note

Funding Information:
The authors acknowledge the support of the Research Foundation Flanders (FWO) under Grant No. G.0D86.16N , and of the Russian Academic Excellence Project ‘ 5-100 ’. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 817762 ).

Publisher Copyright:
© 2021 Elsevier Inc.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

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title = "T-structures and twisted complexes on derived injectives",

abstract = "In the paper {"}Deformation theory of abelian categories{"}, the last two authors proved that an abelian category with enough injectives can be reconstructed as the category of finitely presented modules over the category of its injective objects. We show a generalization of this to pretriangulated dg-categories with a left bounded non-degenerate t-structure with enough derived injectives, the latter being derived enhancements of the injective objects in the heart of the t-structure. Such dg-categories (with an additional hypothesis of closure under suitable products) can be completely described in terms of left bounded twisted complexes of their derived injectives.",

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year = "2021",

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doi = "10.1016/j.aim.2021.107826",

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AU - Lowen, Wendy

AU - Van den Bergh, Michel

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Y1 - 2021/8/27

N2 - In the paper "Deformation theory of abelian categories", the last two authors proved that an abelian category with enough injectives can be reconstructed as the category of finitely presented modules over the category of its injective objects. We show a generalization of this to pretriangulated dg-categories with a left bounded non-degenerate t-structure with enough derived injectives, the latter being derived enhancements of the injective objects in the heart of the t-structure. Such dg-categories (with an additional hypothesis of closure under suitable products) can be completely described in terms of left bounded twisted complexes of their derived injectives.

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T-structures and twisted complexes on derived injectives

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