2002 Fiscal Year Final Research Report Summary
Analysis of Filtrations in Local Rings and the Associated graded rings
| Project/Area Number |
11640011
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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 | CHIBA UNIVERSITY |
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Principal Investigator |
NISHIDA Koji Chiba University, Graduate School of Science and Technology, Associate Professor, 大学院・自然科学研究科, 助教授 (60228187)
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| Co-Investigator(Kenkyū-buntansha) |
SUGIYAMA Ken-ichi Chiba University, Fuculty of Science, Associate Professor, 理学部, 助教授 (90206441)
KURANO Kazuhiko Tokyo Met. University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90205188)
KOSHITANI Shigeo Chiba University, Faculty of Science, Professor, 理学部, 教授 (30125926)
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| Project Period (FY) |
1999 – 2002
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| Keywords | Local Ring / Graded Ring / Homology |
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| Research Abstract |
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.
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