Silting reduction and Calabi–Yau reduction of triangulated categories

Iyama, Osamu; Yang, Dong

doi:10.1090/tran/7213

Silting reduction and Calabi–Yau reduction of triangulated categories
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Trans. Amer. Math. Soc. 370 (2018), 7861-7898 Request permission

Abstract:

We study two kinds of reduction processes of triangulated categories, that is, silting reduction and Calabi–Yau reduction. It is shown that the silting reduction $\mathcal {T}/\mathsf {thick}\mathcal {P}$ of a triangulated category $\mathcal {T}$ with respect to a presilting subcategory $\mathcal {P}$ can be realized as a certain subfactor category of $\mathcal {T}$, and that there is a one-to-one correspondence between the set of (pre)silting subcategories of $\mathcal {T}$ containing $\mathcal {P}$ and the set of (pre)silting subcategories of $\mathcal {T}/\mathsf {thick}\mathcal {P}$. This result is applied to show that the Amiot–Guo–Keller construction of $d$-Calabi–Yau triangulated categories with $d$-cluster-tilting objects takes silting reduction to Calabi–Yau reduction.

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