Studies of the structure of triangulated categories associated with noncommutative graded isolated singularities
Project/Area Number |
15K17503
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
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Research Institution | Hirosaki University |
Principal Investigator |
Ueyama Kenta 弘前大学, 教育学部, 講師 (30746409)
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Project Period (FY) |
2015-04-01 – 2018-03-31
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Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | 非可換次数付き孤立特異点 / 三角圏 / 安定圏 / 非可換射影スキーム / 非可換射影空間 / AS-regular algebra / 非可換次数付孤立特異点 / 非可換代数幾何学 / AS-Gorenstein algebra / 非可換超曲面 / Calabi-Yau algebra / superpotential |
Outline of Final Research Achievements |
Triangulated categories are increasingly important in many areas of mathematics including algebraic geometry and representation theory of algebras. In particular, triangulated categories associated with isolated singularities have made rapid progress. In this research, I studied noncommutative graded isolated singularities, and abelian categories and triangulated categories associated with them. As main achievements, I proved that the stable category of graded maximal Cohen-Macaulay modules over an AS-Gorenstein isolated quotient singularity has a tilting object and therefore it is triangle equivalent to the derived category of a finite dimensional algebra. Also I gave conditions for the noncommutative projective scheme associated with a noncommutative graded isolated singularity to be realized as a noncommutative projective space.
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Report
(4 results)
Research Products
(21 results)