| 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)
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| 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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