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
The classification of homogeneous Cohen-Macaulay rings of finite representation type
✍ Scribed by David Eisenbud; Jürgen Herzog
- Publisher
- Springer
- Year
- 1988
- Tongue
- English
- Weight
- 366 KB
- Volume
- 280
- Category
- Article
- ISSN
- 0025-5831
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📜 SIMILAR VOLUMES
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.
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 singular