Simple General Neron Desingularization in local Q-algebras

Abstract

We give here a easier proof of the so-called General Neron Desingularization in the frame of local algebras.

On a question of Swan. With an Appendix by Kęstutis Česnavičius

“…Theorem 11. (General Néron Desingularization, Popescu [20], [21], [22], [23], [24], André [2], Swan [30]) Let u : A → A ′ be a regular morphism of Noetherian rings and B an A-algebra of finite type. Then any A-morphism v :…”

Valuation rings of dimension one as limits of smooth algebras

“…The proof goes as in the above theorem. We need the following lemma ([12, Lemma 7] which is an extension of [5, Proposition 3], and [11,Proposition 5]).…”