Coefficient fields for plane curves. (English) Zbl 0703.13020
One gives characterizations of the dimension one complete equicharacteristic reduced noetherian local rings (R,m) with integral closure \((R',m')\) for which there exist coefficient fields k for R and \(k'\) for \(R'\) such that \(k\subset k'\) and \(R\otimes_ kk'\) is analytically unramified. The interest of these rings lies in the examples given by S. S. Abhyankar of irreducible curves to show that the notion of singularity of dimensional type 1 introduced by O. Zariski is specific to zero characteristic.
Reviewer: N.Manolache
MSC:
13H10 | Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) |
14H20 | Singularities of curves, local rings |
14M05 | Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) |
Keywords:
dimension one complete equicharacteristic reduced noetherian local rings; coefficient fields; singularity of dimensional type 1References:
[1] | Abhyankar S. S., A. J. M 90 pp 346– (1968) |
[2] | Abhyankar S. S., Proc. Symp. in Pure Math. A. M. S 40 (1983) |
[3] | Campillo A., Proc. Symp. in Pure Math. A. M. S 40 (1983) |
[4] | Campillo A., To appear on Publication of the Branch Center (1985) |
[5] | Granja A., Ph.D. Thesis. Valladolid University (1985) |
[6] | Nagata, M. 1962. ”Local Rings””. Edited by: Interscience Publishers. · Zbl 0123.03402 |
[7] | Zariski O., A. J. M 87 pp 507– (1965) |
[8] | Zariski O., A. J. M 87 pp 972– (1965) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.