WebA-module. If M= mM, then M= 0. Hint. Induct on the number of generators of M. 1. Caleb Ji Cohen-Macaulay rings and schemes Summer 2024 ... If Ais Cohen-Macaulay, then … WebRecall that if R is a local ring, then a finitely generated R-module N is called a maximal Cohen-Macaulay module (abbreviated MCM) if depth(N)=dim(R). Let S be a regular local ring and suppose that M is a finitely generated Cohen- Macaulay S-module of codimension c. Given a regular sequence f 1 ,...,f cin the annihilator of M, so that M is a …
Cohen-Macaulay ring - Encyclopedia of Mathematics
WebA Noetherian local ring is called Cohen-Macaulay if it is Cohen-Macaulay as a module over itself. Note that this is equivalent to requiring the existence of a -regular sequence of … WebSome time ago the authors had been looking at explicit DG-models for certain stable categories of maximal Cohen-Macaulay models (based on Theorem 1.1). We knew that Proposition 1.3 was true in the 3-dimensional case (as then it is a consequence of Proposition 1.2 ) and expected a suitable generalization to hold in higher dimension as well. st mary the virgin dover
Torsion-free Cohen-Macaulay modules - Mathematics Stack …
WebAuslander and Buchweitz have proved that every finitely generated module over a Cohen–Macaulay (CM) ring with a dualizing module admits a so-called maximal CM approximation. In terms of relative homological algebra, this means that every finitely generated module has a special maximal CM precover. In this paper, we prove the … WebThe central objects of study are maximal Cohen–Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. Webessary and sufficient condition for a Cohen-Macaulay R-module to have only one nonvanishing local cohomology. 4.6. Corollary. Assume that M is a Cohen-Macaulay R … st mary the virgin english bicknor