Analysis of Filtrations in Local Rings and the Associated graded rings

局部环和相关分级环的过滤分析

• 批准号: 11640011
• 负责人: NISHIDA Koji
• 金额: $ 2.3万
• 依托单位: CHIBA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640011/
• 关键词: Local Ring; Graded Ring; Homology; フィルトレーション; ホモロジー代数; 次数付主環

In this research we aimed to study homological property of the form ring associated to a general filtration F : A = F_0 ⊇ F_1 ⊇ F_2 ⊇ ・・・ in a local ring A. For that purpose we have introduced the notion of analytic deviation of F, which was originally defined for ideals, and proceeded with the research regarding analytic deviation as a barometer of difficulty of analysis. Our main results obtained in each year were as follows.1. (1999) A theory for filtrations of analytic deviation zero was established.2. (2000) A criterion for Cohen-Macaulay property of the form ring associated to a filtration of analytic deviation one was given.3. (2001) We have applied our theory stated above to various filtrations.4. (2002) We gave a theory in the case where the analytic deviation was arbitrary.

在本研究中，我们旨在研究与一般过滤F相关的形式环的同调性质：a = F_0在局部环a中，我们引入了F的解析偏差的概念，该概念最初是为理想而定义的，并将解析偏差作为分析难度的指标进行了研究。我们每年取得的主要成果如下：（1999）建立了分析偏差为零的滤波理论。（2000）给出了与解析偏差1的过滤有关的形式环的Cohen-Macaulay性质的判据。（2001）我们已经将上述理论应用于各种过滤。（2002）在分析偏差是任意的情况下，我们给出了一个理论。

项目成果

Koji Nishida: "On filtrations having small analytic deviation"Comm.Algebra. 29. 2711-2729 (2001)

Koji Nishida：“关于具有小分析偏差的过滤”Comm.Algebra。

Koji Nishida: "On the integral closure of certain ideals fenerated by regular sequences"Journal of Pure and Applted Algebra. (発表予定).

Koji Nishida：“论正则序列的某些理想的积分封闭”《纯粹与应用代数杂志》（待出版）。

GOTO, Shiro: "Hilbert coefficients and Buchsbaumness of associated graded rings"J. Pure and Appl. Algebra. to appear.

后藤四郎：“相关分级环的希尔伯特系数和布克斯鲍姆性”J。

Koji Nishida: "On filtrations having small analytic deviation"Communications in Algebra. (発表予定).

Koji Nishida：“关于具有小分析偏差的过滤”代数通讯（待提交）。

Koji Nishida: "Hilbert-Samuel function and Grothendieck group"Proc.Edinburgh Math.Soc.. 43. 73-94 (2000)

Koji Nishida：“Hilbert-Samuel 函数和 Grothendieck 群”Proc.Edinburgh Math.Soc.. 43. 73-94 (2000)