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Letter to the editor: General Néron desingularization and approximation

Published online by Cambridge University Press:  22 January 2016

Dorin Popescu
Dorin Popescu*
Affiliation:
Department of Mathematics, INCREST, Bdul Păcii 220, 79622, Bucharest, Romania
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This letter concerns our papers [4], [5] and its aim is to give a simplification to the proof of the General Néron Desingularization (see [5] (2.4) or here below) together with a small reparation; as T. Ogoma pointed out in [3], our Lemma (9.5) from [4] does not hold in the condition iii2) (this is true because the “changing” from line 5 from down the page 123 [4] may not preserve iii2)). However our results were not affected in characteristic zero (they use just iii1) from [4] (9.5)). In [3] Ogoma gives a nice simplification of our proof.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 118 , June 1990 , pp. 45 - 53
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[1] Matsumura, H., Commutative Algebra, Benjamin, New-York, 1980.Google Scholar
[2] Nica, V. and Popescu, D., A structure Theorem on formally smooth morphisms in positive characteristic, J. Algebra, 100 (1986), 436–455.Google Scholar
[3] Ogoma, T., General Néron Desingularization based on idea of Popescu, Preprint 1988.Google Scholar
[4] Popescu, D., General Néron desingularization, Nagoya Math. J., 100 (1985), 97–126.Google Scholar
[5] Popescu, D., General Néron desingularization and approximation, Nagoya Math. J., 104 (1986), 85–115.CrossRefGoogle Scholar
[6] Raynaud, M., Anneaux henséliens et approximations, in Colloque d’Algébre de Rennes, Publ. Sem. Math. Univ. Rennes, 1972.Google Scholar