Derived equivalences via HRS-tilting

DOI10.1016/J.AIM.2019.106749zbMATH Open1457.18018arXiv1804.05629OpenAlexW2965056405WikidataQ127404799 ScholiaQ127404799MaRDI QIDQ2324584

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Publication date: 11 September 2019

Published in: (Search for Journal in Brave)

Abstract: Let $mathcalA$ be an abelian category and $mathcalB$ be the Happel-Reiten-Smal{o} tilt of $mathcalA$ with respect to a torsion pair. We give necessary and sufficient conditions for the existence of a derived equivalence between $mathcalB$ and $mathcalA$, which is compatible with the inclusion of $mathcalB$ into the derived category of $mathcalA$. In particular, any splitting torsion pair induces a derived equivalence. We prove that for the realization functor of any bounded $t$-structure, its denseness implies its fully-faithfulness.

Full work available at URL: https://arxiv.org/abs/1804.05629

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