Isomorphism of complete local noetherian rings and strong approximation

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)3435-3448
Number of pages14
JournalProceedings of the American Mathematical Society
Volume136
Issue number10
DOIs
StatePublished - Oct 1 2008

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Strong Approximation
Noetherian Ring
Local Ring
Isomorphism
Isomorphic
Approximation Theorem
Maximal Ideal
Strong Theorems

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Isomorphism of complete local noetherian rings and strong approximation. / Van Den Dries, Lou.

In: Proceedings of the American Mathematical Society, Vol. 136, No. 10, 01.10.2008, p. 3435-3448.

Research output: Contribution to journalArticle

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