Closure operations and actions of algebraic groups
| Project/Area Number |
18540025
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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 | Nagoya University |
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Principal Investigator |
HASHIMOTO Mitsuyasu Nagoya University, 大学院・多元数理科学研究科, 准教授 (10208465)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIDA Ken-ichi 名古屋大学, 大学院・多元数理科学研究科, 准教授 (80240802)
OKADA Soichi 名古屋大学, 大学院・多元数理科学研究科, 教授 (20224016)
IYAMA Osamu 名古屋大学, 大学院・多元数理科学研究科, 教授 (70347532)
HAYASHI Takahiro 名古屋大学, 大学院・多元数理科学研究科, 准教授 (60208618)
KURANO Kazuhiko 明治大学, 理工学部, 教授 (90205188)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,150,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥750,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 閉包操作 / 代数群 / Matijevic-Roberts型定理 / Matlis双対性 / 良いフィルター付け / 密着閉包 / 作用 / 同変局所コホモロジー / G局所スキーム / 線型簡約群 / 不変式環 / 不変式論 / G素イデアル / G準素イデアル / G整域 / G局所Gスキーム / G中山の補題 / G局所双対性 / 局所コホモロジー |
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| Research Abstract |
When a group scheme G acts on a commutative rig, we consider the problem, if the result of closure operations on G-ideals again a G-ideal. We get some results in special cases. We also studied basics on equivariant local cohomology, and obtained the equivariant versions of Matlis and the local duality. We also defined the equivariant versions of prime and primary ideals, and obtained the equivariant versions of the existence and the uniqueness of the primary decomposition. We also succeeded in proving the Matijevic-Roberts type theorems on singularities in positive characteristic.
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Report
(6 results)
Research Products
(75 results)
