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Results tagged with flatness
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user 1
13
votes
4
answers
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Does smoothness descend along flat morphisms?
Suppose $f:X\to Y$ is a flat morphism of schemes. If $X$ is smooth at $x$, must $Y$ be smooth at $f(x)$?
If $f$ is locally finitely presented, then it is open (using EGA IV 1.10.4), so after repl …
28
votes
5
answers
9k
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Can a quotient ring R/J ever be flat over R?
If $J\neq J^2$, this sequence is not exact, contradicting flatness of $R/J$.
But sometimes it happens that $J=J^2$, like the case of the maximal ideal of the ring $k[t^q| q\in\mathbf Q_{>0}]$. …