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) |
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Pages (from-to) | 3435-3448 |
Number of pages | 14 |
Journal | Proceedings of the American Mathematical Society |
Volume | 136 |
Issue number | 10 |
DOIs | |
State | Published - Oct 2008 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics