Timeline for regular locus of an affine domain
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6, 2015 at 15:32 | review | Close votes | |||
| Mar 7, 2015 at 13:14 | |||||
| Mar 6, 2015 at 15:18 | comment | added | Karl Schwede | I voted to close this because this is about a basic topic in commutative algebra. | |
| Mar 6, 2015 at 12:47 | comment | added | Vinteuil | The regular locus is open more generally for finite type algebras over a complete local ring (search for "excellent rings" if you want to explore this condition in more generality, for instance in EGA IV, 6 and 7). | |
| Mar 6, 2015 at 11:57 | comment | added | sagnik chakraborty | Can you please tell me a reference for the fact that the regular locus of any affine algebra over a field is open? | |
| Mar 6, 2015 at 11:44 | comment | added | naf | @MatthiasWendt No need to assume characteristic 0. What you say works for any affine algebra over any field. | |
| Mar 6, 2015 at 10:55 | comment | added | Matthias Wendt | Yes, sorry, I missed the affine domain condition. Maybe (assuming characteristic 0) you can use openness of the smooth locus to get a positive answer. I still think that my example gives a negative answer if you omit the condition that $A$ is an affine domain - $\mathfrak{p}=(0)$ and there is only one maximal ideal. | |
| Mar 6, 2015 at 10:24 | comment | added | sagnik chakraborty | I need some maximal ideal (not all!) containing the prime ideal. Sorry to say, but you've also failed to understand the question! | |
| Mar 6, 2015 at 10:15 | comment | added | Matthias Wendt | How about taking the localization of $k[X,Y]/(Y²-X²(X+1))$ at the nodal singularity? The result is local ring of dimension 1 which is not regular. However, the field of fractions is a regular local ring. This should be a negative answer to the question. | |
| Mar 6, 2015 at 10:05 | comment | added | sagnik chakraborty | Don't understand why people are in such a hurry to reply without even understanding the question! | |
| Mar 6, 2015 at 8:50 | history | asked | sagnik chakraborty | CC BY-SA 3.0 |