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arXiv · 1611.08139

Torsion pairs in silting theory

Lidia Angeleri Hügel·Frederik Marks·Jorge Vitória
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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.

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Lidia Angeleri Hügel, Frederik Marks, Jorge Vitória. 2016-11-24. Torsion pairs in silting theory. https://doi.org/10.2140/pjm.2017.291.257

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