| Project/Area Number |
20540037
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
HOSHINO Mitsuo University of Tsukuba, 大学院・数理物質科学研究科, 講師 (90181495)
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| Co-Investigator(Kenkyū-buntansha) |
FUJITA Hisaaki 筑波大学, 大学院・数理物質科学研究科, 准教授 (60143161)
ABE Hiroki 筑波大学, 大学院・数理物質科学研究科, 準研究員 (20533342)
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| Research Collaborator |
KOGA Hirotaka 筑波大学, 大学院・数理物質科学研究科, 博士後期課程1年
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 多元環の表現論 / ゴレンシュタイン環 / アウスランダー・ゴレンシュタイン環 / アウスランダー・ゴレンシュタイン分解 / ゴレンシュタイン多元環 / ゴレンシュタイン整環 / 行列環 / 導来圏 / 導来同値 / セール双対 |
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| Research Abstract |
We extended Serre duality theory in algebraic geometry to Noether algebras and, using this notion, we characterized Gorensteinness of Noether algebras and provided a necessary and sufficient condition for a tilting complex over a Gorenstein algebra to have a Gorenstein algebra as an endomorphism algebra. Here, a Noether algebra is a module-finite algebra over a commutative Noether ring and is said to be a Gorenstein algebra if its dual over a Gorenstein base ring in the derived category is a shifted projective generator.
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