Frank
|
Registered User
|
|
|
Feb 6 |
awarded | ● Nice Question |
|
Jan 5 |
revised |
Is $R=k[x_1,\ldots]\to k[[x_1,\ldots]]$ a flat morphism? What about $R\to\hat{R}$? added 501 characters in body; edited title; added 1 characters in body |
|
Jan 2 |
comment |
Is $R=k[x_1,\ldots]\to k[[x_1,\ldots]]$ a flat morphism? What about $R\to\hat{R}$? Right, I was not aware of this difference between the definition of the formal power series in infinitely many variables (i.e. which contains $\sum x_i$) as opposed to the completion of $k[x_1,\ldots]$ at $(x_1,\ldots)$ (which does not). Now that this is clear, I suppose it's not clear whether either of the two morphisms are flat! |
|
Jan 2 |
comment |
Is $R=k[x_1,\ldots]\to k[[x_1,\ldots]]$ a flat morphism? What about $R\to\hat{R}$? I'm a bit confused about your second statement if you wouldn't mind elaborating. I am taking the completion of $k[x_1,\ldots]$ along the ideal $(x_1,\ldots)$ which is nothing other than $k[[x_1,\ldots]]$. |
|
Jan 2 |
revised |
Is $R=k[x_1,\ldots]\to k[[x_1,\ldots]]$ a flat morphism? What about $R\to\hat{R}$? added 118 characters in body |
|
Jan 2 |
revised |
Is $R=k[x_1,\ldots]\to k[[x_1,\ldots]]$ a flat morphism? What about $R\to\hat{R}$? deleted 1 characters in body |
|
Jan 2 |
comment |
Is $R=k[x_1,\ldots]\to k[[x_1,\ldots]]$ a flat morphism? What about $R\to\hat{R}$? Indeed! Or more generally, if $R$ is a regular coherent ring and $m$ a maximal ideal, is the completion $\hat{R}$ along $m$ a flat $R$-module? |
|
Jan 2 |
asked | Is $R=k[x_1,\ldots]\to k[[x_1,\ldots]]$ a flat morphism? What about $R\to\hat{R}$? |
|
Nov 28 |
comment |
$n$-path-connected components of a variety The answer to question 1 is Lemma 3.9 here arxiv.org/abs/1208.4055 |
