Timeline for Completion of a completion
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 10, 2012 at 11:09 | comment | added | François Brunault | If $I$ is of finite type then $\widehat{I} = I \widehat{A}$ (more generally if $M$ is a f.g. $A$-module then $M \otimes \widehat{A} \to \widehat{M}$ is surjective. This is indeed false in general, for example you can take $A=k[X_1,X_2,\ldots]$ and $I=\langle X_1,X_2,\ldots \rangle$. Then $F = X_1+X_2^2+\cdots \in \widehat{I}$ doesn't belong to the image of $I$. | |
| Oct 10, 2012 at 9:49 | comment | added | DARK | Just to be sure, are you claiming that my question has a negative answer in general? | |
| Oct 10, 2012 at 9:27 | history | answered | Anton Fonarev | CC BY-SA 3.0 |