| Project/Area Number |
22540046
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIDA Ken-ichi 日本大学, 文理学部, 教授 (80240802)
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| Co-Investigator(Renkei-kenkyūsha) |
MIYAZAKI Mitsuhiro 京都教育大学, 教育学部, 准教授 (90219767)
KURANO Kazuhiko 明治大学, 理工学部, 教授 (90205188)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 可換環論 / 不変式論 / 亜主束 / Frobenius 写像 / F-signature / 不変式環 / Cox環 / 因子類群 / 正準加群 / 小行列式 / 極小自由分解 / 同変全商環 / 簡約群 / 良いフィルター付け / 強F正則性 / 一意分解整域 |
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| Research Abstract |
Let G be a reductive group over a field of positive characteristic, acting on a polynomial ring S linearly. We proved that if S has a good filtration as a representation of G, then for any parabolic subgroup P of G, the invariant subring S^{U_P} under the action of the unipotent radical U_P of P is a finitely generated strongly F-regular UFD, in particular, it is Gorenstein. We also discussed properties of commutative rings of positive characteristic, and jointly with Mitsuhiro Miyazaki, we discussed G-prime and G-primary G-ideals. These are studies in commutative algebra and invariant theory.
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