caa a22 4500 445836253 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00209-009-0624-6 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0624-6 About de Smit's question on flatness [Elektronische Daten] [Sylvain Brochard, Ariane Mézard] Let $${\varphi : A \rightarrow B}$$ be a flat morphism of Artin local rings with the same embedding dimension. Denote by $${\mathfrak{m}_A}$$ the maximal ideal of A. Bart de Smit asked whether any finite B-module that is A-flat is B-flat. We prove the conjecture in embedding dimension one or two. In embedding dimension n, we prove the conjecture under an additional assumption on $${B/\mathfrak{m}_{A}B}$$. The Author(s), 2009 Flatness nationallicence Artin rings nationallicence Complete intersections nationallicence Gorenstein rings nationallicence Brochard Sylvain Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden, The Netherlands aut Mézard Ariane Département de mathématiques, Université de Versailles Saint-Quentin, 45, avenue des États-Unis, 78035, Versailles Cedex, France aut Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 385-401 0025-5874 267:1-2<385 2011 267 209 https://doi.org/10.1007/s00209-009-0624-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0624-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brochard Sylvain Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden, The Netherlands aut NATIONALLICENCE 700 1- Mézard Ariane Département de mathématiques, Université de Versailles Saint-Quentin, 45, avenue des États-Unis, 78035, Versailles Cedex, France aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 385-401 0025-5874 267:1-2<385 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer