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Tokyo-Nagoya Algebra Seminar
Seminar information archive ～04/24｜Next seminar｜Future seminars 04/25～
| Organizer(s) | Noriyuki Abe, Aaron Chan, Osamu Iyama, Yasuaki Gyoda, Hiroyuki Nakaoka, Ryo Takahashi |
|---|
2020/12/10
16:30-18:00 Online
Please see the URL below for details on the online seminar.
Hiroki Matsui (University of Tokyo)
Subcategories of module/derived categories and subsets of Zariski spectra (Japanese)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the URL below for details on the online seminar.
Hiroki Matsui (University of Tokyo)
Subcategories of module/derived categories and subsets of Zariski spectra (Japanese)
[ Abstract ]
The classification problem of subcategories has been well considered in many areas. This problem is initiated by Gabriel in 1962 by giving a classification of localizing subcategories of the module category Mod R via specialization-closed subsets of the Zariski spectrum Spec R for a commutative noetherian ring. After that several authors tried to generalize this result in many ways. For example, four decades later, Krause introduced the notion of coherent subsets of Spec R and used it to classify wide subcategories of Mod R. In this talk, I will introduce the notions of n-wide subcategories of Mod R and n-coherent subsets of Spec R for a (possibly infinite) non-negative integer n. I will also introduce the notion of n-uniform subcategories of the derived category D(Mod R) and prove the correspondences among these classes. This result unifies/generalizes many known results such as the classification given by Gabriel, Krause, Neeman, Takahashi, Angeleri Hugel-Marks-Stovicek-Takahashi-Vitoria. This talk is based on joint work with Ryo Takahashi.
[ Reference URL ]The classification problem of subcategories has been well considered in many areas. This problem is initiated by Gabriel in 1962 by giving a classification of localizing subcategories of the module category Mod R via specialization-closed subsets of the Zariski spectrum Spec R for a commutative noetherian ring. After that several authors tried to generalize this result in many ways. For example, four decades later, Krause introduced the notion of coherent subsets of Spec R and used it to classify wide subcategories of Mod R. In this talk, I will introduce the notions of n-wide subcategories of Mod R and n-coherent subsets of Spec R for a (possibly infinite) non-negative integer n. I will also introduce the notion of n-uniform subcategories of the derived category D(Mod R) and prove the correspondences among these classes. This result unifies/generalizes many known results such as the classification given by Gabriel, Krause, Neeman, Takahashi, Angeleri Hugel-Marks-Stovicek-Takahashi-Vitoria. This talk is based on joint work with Ryo Takahashi.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
