Vol. 291, No. 2, 2017

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ISSN: 0030-8730
Torsion pairs in silting theory

Lidia Angeleri Hügel, Frederik Marks and Jorge Vitória

Vol. 291 (2017), No. 2, 257–278
Abstract

In the setting of compactly generated triangulated categories, we show that the heart of a (co)silting t-structure is a Grothendieck category if and only if the (co)silting object satisfies a purity assumption. Moreover, in the cosilting case the previous conditions are related to the coaisle of the t-structure being a definable subcategory. If we further assume our triangulated category to be algebraic, it follows that the heart of any nondegenerate compactly generated t-structure is a Grothendieck category.

Keywords
torsion pair, silting, cosilting, t-structure, Grothendieck category
Mathematical Subject Classification 2010
Primary: 18E15, 18E30, 18E40
Milestones
Received: 24 November 2016
Revised: 22 March 2017
Accepted: 11 April 2017
Published: 14 September 2017
Authors
Lidia Angeleri Hügel
Dipartimento di Informatica, Settore di Matematica
Università degli Studi di Verona
Strada Le Grazie 15
Ca’ Vignal 2
I-37134 Verona
Italy
Frederik Marks
Institut für Algebra und Zahlentheorie
Universität Stuttgart
Pfaffenwaldring 57
D-70569 Stuttgart
Germany
Jorge Vitória
Department of Mathematics
City University of London
Northampton Square
EC1V 0HB
United Kingdom