| Budget Amount *help |
¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
One of the important conjectures in modular representation theory of finite groups is Broue's abelian defect group conjecture. It states that the principal blocks of two finite groups having a common abelian Sylow subgroup and the same fusion systems on the Sylow subgroup should be derived equivalent.To solve the conjecture it is important to develope the way of gluing local derived equivalences to global stable equivalences and of lifting stable equivalences to derived equivalences. In this project, related to gluing processes I obtained a result for Brauer indecomposability of Scott modules with abelian vertex, and then generalize this result to non-abelian vertex case. I also tried to apply these results to obtain new examples of derived equivalences with non-abelian defect groups and Morita equivalences for infinite series of finite groups.
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