Analysis of Filtrations in Local Rings and the Associated graded rings

点击翻译按钮获取中文摘要

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.