COHEN-MACAULAY MODULES AND HOLONOMIC MODULES OVER FILTERED RINGS
Miyahara, Hiroaki and Nishida, Kenji COHEN-MACAULAY MODULES AND HOLONOMIC MODULES OVER FILTERED RINGS. In: 第12回代数学若手研究会, March 3--5, 2007., 千葉大学理学部.
We study Gorenstein dimension and grade of a module M over a ltered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a ltered module and its associated graded module is the most valuable property for an investigation of ltered rings. We prove an inequality G-dimM G-dim grM and an equality gradeM = grade grM, whenever Gorenstein dimension of grM is nite (Theorems 2.3 and 2.8). We would say that the use of G-dimension adds a new viewpoint for studying ltered rings and modules. We apply these results to a ltered ring with a Cohen-Macaulay or Gorenstein associated graded ring and study a Cohen-Macaulay, perfect or holonomic module.