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arXiv · 1804.05629

Derived equivalences via HRS-tilting

Xiao-Wu Chen·Zhe Han·Yu Zhou
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Abstract

Let $\mathcal{A}$ be an abelian category and $\mathcal{B}$ be the Happel-Reiten-Smal{\o} tilt of $\mathcal{A}$ with respect to a torsion pair. We give necessary and sufficient conditions for the existence of a derived equivalence between $\mathcal{B}$ and $\mathcal{A}$, which is compatible with the inclusion of $\mathcal{B}$ into the derived category of $\mathcal{A}$. 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.

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Xiao-Wu Chen, Zhe Han, Yu Zhou. 2018-04-16. Derived equivalences via HRS-tilting. https://arxiv.org/abs/1804.05629

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