Study of excellent rings and its neighborhood

优良环及其邻域研究

• 批准号: 16540032
• 负责人: KAWASAKI Takesi
• 金额: $ 2.3万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540032/
• 关键词: excellent rings; Cohen-Macaulay rings; Cousin complex; canonical module; annihilator theorem; Briancon-Skodaの定理; 局所コホモロジー; コーエン・マコーレー環

(1) In [K], I gave a necessarily and sufficient condition for a Noetherian ring to have an arithmetic Cohen-Macaulayfication.I refine its construction by introducing a new notion, called p-standard sequences.(2) In [K], computed the depth of the canonical module. I compute local cohomology modules of the canonical module.(3) In 1978, Faltings prove the annihilator theorem. In 1982, he conjectured that the annihilator theorem holds under weaker assumption. I give an affirmative answer to his conjecture.(4) In 1991, Hukene [H] proved the uniform Artin-Rees theorem and the uniform Briancon-Skoda theorem. He also conjectured that these theorem hold under weaker assumption. I give an affirmative answer to [H, Conjecture 2.13] concerning these theorems.[F1] G.Faltings, Ueber die Annulatoren lokaler Kohomologiegruppen, Arch.Math. (Basel) 30 (1978), 473--476.[F2] G.Faltings, Der Endlichkeitssatz in der lokalen Kohomologie, Math.Ann.255 (1981), 45--56.[H] C.Huneke, Uniform bounds in noetherian rings, Invent.Math. 107 (1992), 203--223.[K] T.Kawasaki, Finiteness of Cousin cohomologies.

(1)在[K]中，给出了noether环具有算术Cohen-Macaulayfication的充分必要条件。我通过引入一个新的概念来完善它的构造，叫做p标准序列。(2)在[K]中，计算正则模块的深度。我计算正则模的局部上同模。(3) 1978年，Faltings证明了湮灭子定理。1982年，他推测湮灭子定理在较弱的假设下成立。我对他的猜想给予肯定的答复。(4) 1991年，Hukene [H]证明了一致Artin-Rees定理和一致Briancon-Skoda定理。他还推测这些定理在较弱的假设下成立。关于这些定理，我给[H，猜想2.13]一个肯定的答案。[1]王晓明，王晓明，王晓明，等。（巴塞尔）30(1978),473—476。[2]王晓东，王晓东，王晓东，等。一种基于正则表达式的正则表达式。数学学报（自然科学版），2004(1981), 45 - 56。[H]张晓明，周晓明，周晓明，等。107(1992), 203—223。[K]陈志强，表上同调的有限性。