Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T07:11:12.478Z Has data issue: false hasContentIssue false
  • English
  • Français

General Néron desingularization

Published online by Cambridge University Press:  22 January 2016

Dorin Popescu
Dorin Popescu*
Affiliation:
INCREST Department of Mathematics, Bd. Păcii 220, 79622 Bucharest, Romania and Institute of Mathematics, Str. Academiei 14 70109 Bucharest, Romania
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R⊂ R′ be an “unramified” extension of discrete valuation rings in the sense that a local parameter p of R is also a local parameter in R⊂. Suppose that the inclusion R→R⊂ induces separable extensions on fraction and residue fields.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 100 , December 1985 , pp. 97 - 126
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[A] Artin, M., Algebraic structure of power series rings, Contemp. Math. Soc, Providence (1982), 223–227.Google Scholar
[AD] Artin, M. and Denef, J., Smoothing of a ring homomorphism along a section, Arithmetic and Geometry, vol. II, Birkhauser, Boston (1983), 5–32.Google Scholar
[CP] Cipu, M. and Popescu, D., Some extensions of Néron’s p-desingularization and approximation, Rev. Roumaine Math. Pures Appl., t. XXIV, 10 (1981), 1299–1304.Google Scholar
[E] Elkik, R., Solutions d’equations à coefficients dans un anneaux hensélien, Ann. Sci. Ecole Norm Sup. 4e serie, t. 6 (1973), 533–604.Google Scholar
[KMPPR] Kurke, H., Mostowski, T., Pfister, G., Popescu, D. and Roczen, M., Die Approximationseigenschaft lokaler Ringe, Lect. Notes in Math., 634, Springer-Verlag, Berlin, 1978.Google Scholar
[M] Matsumura, H., Commutative algebra, Benjamin, New York, 1980.Google Scholar
[N] Néron, A., Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. IHES, 21, 1964.CrossRefGoogle Scholar
[Ni] Nica, V., A desingularization theorem in non normal one dimensional rings, Preprint INCREST nr. 43/1983.Google Scholar
[Pl] Ploski, A., Note on a theorem of M. Artin, Bull. Acad. Polon. des Sci., t. XXII, 11 (1974), 1107–1110.Google Scholar
[P1] Popescu, D., A remark on two dimensional local rings with the property of approximation, Math. Z., 173 (1980), 235–240.Google Scholar
[P2] Popescu, D. Global form of Neron’s p-desingularization, Proceedings “Weak of Algebraic Geometry”, Bucharest, June 30-July 6, 1980, Teubner Texte, Band 40, Leipzig, 1981.Google Scholar
[P3] Popescu, D., Higher dimensional Neron desingularization and approximation Preprint INCREST nr. 50/1982.Google Scholar
[P4] Popescu, D., On Zariski’s Uniformization Theorem, Algebraic Geometry, Bucharest 1982, Proceedings, Lect. Notes in Math., 1056, Springer-Verlag, Berlin, 1984.Google Scholar
[Z] Zariski, O., Local uniformization on algebraic varieties, Ann. of Math., 41 (1940).Google Scholar