Isomorphism of complete local noetherian rings and strong approximation

Lou Van Den Dries

Research output: Contribution to journalArticlepeer-review


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
Issue number10
StatePublished - Oct 2008

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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