| Project/Area Number |
16KK0099
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| Research Category |
Fund for the Promotion of Joint International Research (Fostering Joint International Research)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
Takahashi Ryo 名古屋大学, 多元数理科学研究科, 准教授 (40447719)
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| Project Period (FY) |
2017 – 2019
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥13,260,000 (Direct Cost: ¥10,200,000、Indirect Cost: ¥3,060,000)
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| Keywords | Cohen-Macaulay加群 / Cohen-Macaulay環 / Gorenstein環 / 可算CM表現型 / Grothendieck群 / 凸錐 / 数値的同値 / 極大Cohen-Macaulay加群 / 因子類群 / 代数学 / 可換環論 / 加群圏 / 部分圏 |
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| Outline of Final Research Achievements |
Various results are obtained. In particular, many properties of the structure of Cohen-Macaulay modules are clarified. A Cohen-Macaulay local ring is said to have finite CM+ representation type if there are only finitely many indecomposable Cohen-Macaulay modules whose nonfree loci have positive dimension. For a Gorenstein ring of dimension one, it is proved that having finite CM+ representation type is equivalent to having either an isolated singularity or countable CM representation type. Consider the Grothendieck group of finitely generated modules modulo the subgroup spanned by pseudo-zero modules. Tensor the real number field and consider the convex cone spanned by Cohen-Macaulay modules. Various topological properties on this convex cone are obtained.
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| Academic Significance and Societal Importance of the Research Achievements |
与えられたCohen-Macaulay環の上のCohen-Macaulay加群全体がもつ構造を調べる研究は「Cohen-Macaulay表現論」とも呼ばれ、可換環論や環の表現論におけるもっとも中心的なテーマの一つであり、世界各国の多くの数学者によってさかんに研究されている。本研究成果はこの理論の研究に大いに寄与するものである。
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