𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Local Rings of Finite Cohen–Macaulay Type

✍ Scribed by Roger Wiegand

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
191 KB
Volume
203
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let R, m be a local Cohen᎐Macaulay ring whose m-adic completion R has an isolated singularity. We verify the following conjecture of F.-O. Schreyer: R has finite Cohen᎐Macaulay type if and only if R has finite Cohen᎐Macaulay type. We ww xx Ž . also show that the hypersurface k x , . . . , x r f has finite Cohen᎐Macaulay 0 d s ww xx Ž . s type if and only if k x , . . . , x r f has finite Cohen᎐Macaulay type, where k 0 d

is the separable closure of the field k.

📜 SIMILAR VOLUMES

Ascent of Finite Cohen–Macaulay Type
Ascent of Finite Cohen–Macaulay Type
✍ Graham Leuschke; Roger Wiegand 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 98 KB

In 1987 F.-O. Schreyer conjectured that a local ring R has finite Cohen-Macaulay type if and only if the completion R has finite Cohen-Macaulay type. We prove the conjecture for excellent Cohen-Macaulay local rings and also show by example that it can fail in general.

On Cohen–Macaulay Rings of Invariants
On Cohen–Macaulay Rings of Invariants
✍ M Lorenz; J Pathak 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 148 KB

We investigate the transfer of the Cohen᎐Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group action. As an illustration, we discuss the special case of mul

Cohen–Macaulay Properties of Ring Homomo
Cohen–Macaulay Properties of Ring Homomorphisms
✍ Luchezar L. Avramov; Hans-Bjørn Foxby 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 454 KB

Numerical invariants which measure the Cohen Macaulay character of homomorphisms .: R Ä S of noetherian rings are introduced and studied. Comprehensive results are obtained for homomorphisms which are locally of finite flat dimension. They provide a point of view from which a variety of phenomena re

Quasi Cohen–Macaulay Properties of Local
Quasi Cohen–Macaulay Properties of Local Homomorphisms
✍ Anders Frankild 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 181 KB

For a large class of local homomorphisms : R ª S, including those of finite w Ž . G-dimension studied by Avramov and Foxby Proc. London Math. Soc. 75 1997 , x 241᎐270 , we assign a new numerical invariant called the quasi Cohen᎐Macaulay defect of , and a local homomorphism is called quasi Cohen᎐Maca

On the Cohen–Macaulay Property of Modula
On the Cohen–Macaulay Property of Modular Invariant Rings
✍ Gregor Kemper 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 203 KB

If V is a faithful module for a finite group G over a field of characteristic p, then the ring of invariants need not be Cohen᎐Macaulay if p divides the order of G. In this article the cohomology of G is used to study the question of Cohen᎐Macaulayness of the invariant ring. One of the results is a