# The HRS tilting process and Grothendieck hearts of t-structures

21 Jun 2020 Parra Carlos E. Saorín Manuel

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... (read more)

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# Categories

• REPRESENTATION THEORY
• CATEGORY THEORY
• RINGS AND ALGEBRAS