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Transactions of the American Mathematical Society

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Silting reduction and Calabi-Yau reduction of triangulated categories


Authors: Osamu Iyama and Dong Yang
Journal: Trans. Amer. Math. Soc. 370 (2018), 7861-7898
MSC (2010): Primary 16E35, 18E30, 16G99, 13F60
DOI: https://doi.org/10.1090/tran/7213
Published electronically: May 3, 2018
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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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Additional Information

Osamu Iyama
Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602 Japan
Email: iyama@math.nagoya-u.ac.jp

Dong Yang
Affiliation: Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing 210093, People’s Republic of China
Email: yangdong@nju.edu.cn

DOI: https://doi.org/10.1090/tran/7213
Keywords: Silting subcategory, silting reduction, cluster tilting subcategory, Calabi--Yau reduction, Amiot--Guo--Keller cluster category, co-t-structure, t-structure.
Received by editor(s): February 20, 2016
Received by editor(s) in revised form: January 27, 2017, and February 15, 2017
Published electronically: May 3, 2018
Additional Notes: The first author acknowledges financial support from JSPS Grant-in-Aid for Scientific Research (B) 24340004, (C) 23540045, and (S) 22224001.
The second author acknowledges financial support from a JSPS postdoctoral fellowship program (P12318) and from the National Science Foundation of China No. 11371196 and No. 11301272
Article copyright: © Copyright 2018 American Mathematical Society

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