t-structures on stable infinity-categories

Fosco Loregian

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arXiv · 2005.14295

t-structures on stable infinity-categories

Fosco Loregian

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Abstract

The present work re-enacts the classical theory of t-structures reducing the classical definition given in *Faisceaux Pervers* to a rather primitive categorical gadget: suitable reflective factorization systems. This translation is only possible due to the virtues of the infinity-categorical setting. Once the basic theory of t-structure has been developed, a natural direction of research is to develop a comprehensive treatment of t-structure in the "torsio-centric" perspective: we apply the technology of factorization systems to the theory of Postnikov towers, to the proof of the abelianity of the heart of a t-structure, and to the theory of Bridgeland's stability conditions.

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Fosco Loregian. 2020-05-28. t-structures on stable infinity-categories. https://arxiv.org/abs/2005.14295

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