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- W4287901531 abstract "In this paper we revisit the problem of determining when the heart of a t-structure is a Grothendieck category, with special attention to the case of the Happel-Reiten-Smal{o} (HSR) t-structure in the derived category of a Grothendieck category associated to a torsion pair in the latter. We revisit the HRS tilting process deriving from it a lot of information on the HRS t-structures which have a projective generator or an injective cogenerator, and obtain several bijections between classes of pairs $(mathcal{A},mathbf{t})$ consisting of an abelian category and a torsion pair in it. We use these bijections to re-prove, by different methods, a recent result of Tilting Theory and the fact that if $mathbf{t}=(mathcal{T},mathcal{F})$ is a torsion pair in a Grothendieck category $mathcal{G}$, then the heart of the associated HRS t-structure is itself a Grothendieck category if, and only if, $mathbf{t}$ is of finite type. We survey this last problem and recent results after its solution." @default.
- W4287901531 created "2022-07-26" @default.
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- W4287901531 date "2020-01-23" @default.
- W4287901531 modified "2023-09-24" @default.
- W4287901531 title "The HRS tilting process and Grothendieck hearts of t-structures" @default.
- W4287901531 doi "https://doi.org/10.48550/arxiv.2001.08638" @default.
- W4287901531 hasPublicationYear "2020" @default.
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