About de Smit's question on flatness

作者：Brochard Sylvain^*; Mezard Ariane

来源：Mathematische Zeitschrift, 2011, 267(1-2): 385-401.

DOI：10.1007/s00209-009-0624-6

• Flatness
• Artin rings
• Complete intersections
• Gorenstein rings

Let phi : A -> B be a flat morphism of Artin local rings with the same embedding dimension. Denote by 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/m(A)B.

• 出版日期2011-2