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.
Mixed characteristic hypersurfaces of finite Cohen–Macaulay type
✍ Scribed by Graham J. Leuschke
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 264 KB
- Volume
- 167
- Category
- Article
- ISSN
- 0022-4049
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✦ Synopsis
We deÿne the mixed ADE singularities, which are generalizations of the ADE plane curve singularities to the case of mixed characteristic. The ADE plane curve singularities are precisely the equicharacteristic plane curve singularities of ÿnite Cohen-Macaulay type; we show that the mixed ADE singularities also have ÿnite Cohen-Macaulay type.
📜 SIMILAR VOLUMES
We say that a Cohen-Macaulay poset (partially ordered set) is "superior" if every open interxal \((x, y)\) of \(P^{*}\) with \(\mu_{p}(x, y) \neq 0\) is doubly Cohen-Macaulay. For example, if \(L=P^{\wedge}\) is a modular lattice, then the Cohen-Macaulay poset \(P\) is superior. We present a formula
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