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Cohen-Macaulay differential graded modules and negative Calabi-Yau configurations

Monday, July 6th, 2020, 2:00 PM  Zoom 房间号:685 9743 2504
*主持人:周国栋 副教授
*时间:2020年7月6日 14:00-15:00
*地点:Zoom 房间号:685 9743 2504 会议密码:164921

晋海波,2016年硕士毕业于华东师范大学,即将博士毕业日本名古屋大学,导师国际数学家大会45分钟报告人日本名古屋大学Osamu Iyama教授。

In this talk, we introduce a nice class of dg algebras A called Gorenstein and introduce the category CM A of Cohen-Macaulay dg A-modules. We show CM A has a structure of Frobenius extriangulated category, which is introduced by Nakaoka and Palu as a common generalization of exact category and triangulated category. We give an analogue of Buchweitz's equivalence, that is, the stable category of CM A is triangle equivalent to the singularity category. Moreover, we study CM A from a point of view of representation theory, and show that it admits Auslander-Reiten extensions. We give a classification of Auslander-Reiten quivers of CM-finite (in the sense that they have only finitely many indecomposable CM dg modules) d-symmetric dg algebras for positive integer d, which is one of the most basic cases of CM-finite Gorenstein dg algebras.

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