2017 Fiscal Year Annual Research Report
Tilting complex and Perverse equivalence in Representation theory
| Project/Area Number |
17F17814
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| Research Institution | Nagoya University |
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Principal Investigator |
伊山 修 名古屋大学, 多元数理科学研究科, 教授 (70347532)
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| Co-Investigator(Kenkyū-buntansha) |
WONG HON YIN 名古屋大学, 多元数理科学研究科, 外国人特別研究員
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| Project Period (FY) |
2017-11-10 – 2020-03-31
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| Keywords | homological algebra / derived category / silting theory / triangulated category / Serre subcategory / exact category / perverse equivalence / finite group algebras |
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| Outline of Annual Research Achievements |
There are many interesting opportunities presented within the host institution, and I have explored some new collaborations in research within Japan. In particular, I start to look at the structure of differential graded modules as a category. Our current goal is to transfer the machinery of perverse equivalence to the differential graded setting and apply to silting theory. Besides, I have also initiated a project to study Frobenius extriangulated category with Laurent Demonet, in hope to enrich the theory which unify techniques on exact categories and those on triangulated category, both of which are crucial in various aspect of representation theory. Also, I am in the process of writing up two other independent results on group algebras of special linear group of degree 2.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
We have studied some properties of derived category of differential graded modules and identify some questions that need to be addressed to achieve the aim of the project.
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| Strategy for Future Research Activity |
To understand deeper connections between perverse equivalences and silting theory, we will try to establish a parallel notion of Serre subcategory in differential graded setting, or to see why this is not possible. To achieve this a better understanding of category of differential graded modules is needed.
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