Torsion pairs in silting theory

Lidia Angeleri Hügel, Frederik Marks and Jorge Vitória

Vol. 291 (2017), No. 2, 257–278

DOI: 10.2140/pjm.2017.291.257

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