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Study of Rees algebras and form rings

里斯代数和形环的研究

基本信息

批准号：
09640071
负责人：
GOTO Shiro
金额：
$ 1.92万
依托单位：
Meiji University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640071/
关键词：
Buchsbaum ring Cohen-Macaulay ring Gorenstein ring canonical module Rees algebra associated graded ring form ring local cohomology Cohen-Macaulay環随半次数環

项目摘要

What I want to do in my research is to study certain ring-structures (such as Buchsbaumness, Cohen-Macaulayness, or Gorensteinness) of Rees algebras associated to ideals in Noetherian local rings, from the view-point of the corresponding properties of their associated graded rings. In [G1] I gave a characterization for the Rees algebras associated to m-primary ideals of minimal multiplicity in Cohen-Macaulay local rings (A, m) to be Buchsbauxn rings, in terms of the corresponding property of the associated graded rings and the extended Rees algebras as well. As a byproduct of this research I constructed a counterexample to the negative a-invariant conjecture raised by Korb-Nakamura, concerning a question on the Cohen-Macaulayness in Rees algebras. Igave a lecture about the examples in the International Conference on Commutative Algebra in honor of David Buchsbaum (the third period, Genova) in Italy ([G2]). Also, K.Yarnagishi [Y] generalized the techniques in [G1], and gave a striking criterion for the associated graded rings of m-primary ideals in Buchsbaum local rings to be Buchsbaum, in terms of the Buchsbaum invariant. He gave a talk about this criterion at the International Conference on Commutative Algebra in honor of David Buchsbaum (the first period, Catania) in Italy, which I organized as one of the organizers. I am also interested in non-commutative algebra and performed ajoint research with Kenji Nishida. Someof the results will appear in [GN1, GN2].

我的研究想做的是从相关分级环的相应性质的角度来研究与诺特局部环中的理想相关的里斯代数的某些环结构（例如布赫斯鲍姆尼斯、科恩-麦考利尼斯或戈伦斯坦尼斯）。在 [G1] 中，我根据相关分级环和扩展 Rees 代数的相应性质，将与 Cohen-Macaulay 局部环 (A, m) 中最小重数的 m 一次理想相关的 Rees 代数描述为 Buchsbauxn 环。作为这项研究的副产品，我针对 Korb-Nakamura 提出的负 a-不变猜想构建了一个反例，涉及里斯代数中的 Cohen-Macaulayness 问题。我在意大利举行的国际交换代数会议上为纪念 David Buchsbaum（第三期，热那亚）做了关于例子的演讲（[G2]）。此外，K.Yarnagishi [Y] 推广了 [G1] 中的技术，并根据 Buchsbaum 不变量给出了 Buchsbaum 局部环中 m 初级理想的相关分级环为 Buchsbaum 的惊人标准。他在意大利举行的国际交换代数会议（第一期，卡塔尼亚）上发表了关于这个准则的演讲，该会议是我作为组织者之一组织的。我对非交换代数也很感兴趣，并与西田健二进行了联合研究。部分结果将出现在[GN1,GN2]中。