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Answer by Akhil Mathew for On the Geometric Interpretation of the Local...
The flat locus is open in any event under reasonable hypotheses (EGA IV-3, Th. 11.1.1), so being flat "at a point" and "in a neighborhood of a point" are equivalent. Also, this particular result is...
View ArticleOn the Geometric Interpretation of the Local Criterion for Flatness
The local criterion for flatness goes this way:Let $\phi : (A,m)\rightarrow (B,m')$ be a local morphism of local Noetherian rings, and $M$ a finitely generated $B$-module. If $x\in m$ is a non...
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