On the Structure of Calabi-Yau Categories with a Cluster Tilting Subcategory

We prove that for $d\geq 2$, an algebraic $d$-Calabi-Yau triangulated category endowed with a $d$-cluster tilting subcategory is the stable category of a DG category which is perfectly $(d+1)$-Calabi-Yau and carries a non degenerate $t$-structure whose heart has enough projectives.

2000 Mathematics Subject Classification: Primary 18E30, 18E35, 18D20; Secondary 16G30, 16G70.

Keywords and Phrases: Triangulated category, Calabi-Yau property, $t$-structure, DG category, Verdier's quotient, Brown representability theorem.

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