Letter to the editor: General Néron desingularization and approximation. (English) Zbl 0685.14009

A regular local morphism of noetherian rings is a filtered inductive limit of smooth finite type morphisms. This result is the subject of two previous papers [cf. the author, Nagoya Math. J. 100, 97-126 (1985; Zbl 0561.14008) and 104, 85-115 (1986; Zbl 0592.14014)] where many applications are given. Using almost the same ideas T. Ogoma got an important simplification [“General Néron desingularization based on idea of Popescu“ (Preprint 1988)] which also contained a small reparation to our previous proof in nonseparable case. The aim of this note is to give a very easy proof of the above result using our previous papers as well as Ogoma’s simplification.
Reviewer: D.Popescu


14E15 Global theory and resolution of singularities (algebro-geometric aspects)
13E05 Commutative Noetherian rings and modules
14B25 Local structure of morphisms in algebraic geometry: étale, flat, etc.
Full Text: DOI


[1] DOI: 10.1016/0021-8693(86)90087-6 · Zbl 0604.13003
[2] Commutative Algebra (1980)
[3] Nagoya Math. J. 100 pp 97– (1985) · Zbl 0561.14008
[4] Nagoya Math. J. 104 pp 85– (1986) · Zbl 0592.14014
[5] Publ. Sem. Math (1972)
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