Isomorphism of complete local noetherian rings and strong approximation

Lou Van Den Dries

doi:10.1090/S0002-9939-08-09401-X

Isomorphism of complete local noetherian rings and strong approximation

Research output: Contribution to journal › Article

Abstract

About a year ago Angus Macintyre raised the following question. Let A and B be complete local noetherian rings with maximal ideals m and n such that A/mⁿ is isomorphic to B/nⁿ for every n. Does it follow that A and B are isomorphic? We show that the answer is yes if the residue field is algebraic over its prime field. The proof uses a strong approximation theorem of Pfister and Popescu, or rather a variant of it, which we obtain by a method due to Denef and Lipshitz. Examples by Gabber show that the answer is no in general.

Original language	English (US)
Pages (from-to)	3435-3448
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-08-09401-X
State	Published - Oct 1 2008

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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Van Den Dries, L. (2008). Isomorphism of complete local noetherian rings and strong approximation. Proceedings of the American Mathematical Society, 136(10), 3435-3448. https://doi.org/10.1090/S0002-9939-08-09401-X

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