Timeline for Equivariant normalization?
Current License: CC BY-SA 3.0
9 events
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| Oct 20, 2013 at 13:52 | history | edited | David E Speyer | CC BY-SA 3.0 |
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| Oct 18, 2013 at 20:34 | comment | added | Jesko Hüttenhain | Oh, nice. That settles everything. Indeed the field is algebraically closed and I assume the group scheme to be a variety, in particular reduced. So I guess, then it will work all the time. Thanks even more! | |
| Oct 18, 2013 at 13:59 | comment | added | David E Speyer | Two issues: (1) A non-reduced scheme need not have a regular point. This is what it going on in the example: $\mathbb{k}[\epsilon]/\epsilon^p$ has one point, and that point is not regular. (2) The way you are talking about closed points and translation suggests you are working over an algebraically closed ground field. If your points $g$ or $h$ are defined over extensions of the ground field, particularly if they are defined over inseparable extensions, there are more issues. | |
| Oct 18, 2013 at 10:08 | comment | added | Jesko Hüttenhain | I thoroughly believe you, but I don't understand why group varieties in positive characteristic can be singular. Take a $g\in G$ which is a regular point of $G$, at least one of those exists. For any $h\in G$, the action of $gh^{-1}$ on $G$ by left multiplication is an automorphism, and $h$ is the preimage of $g$. Hence, $h$ should also be smooth. Where did I use $\mathrm{char}(\Bbbk)=0$ ? | |
| Oct 18, 2013 at 9:34 | vote | accept | Jesko Hüttenhain | ||
| Oct 17, 2013 at 13:35 | history | edited | David E Speyer | CC BY-SA 3.0 |
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| Oct 16, 2013 at 23:06 | comment | added | Peter Samuelson | I think you were supposed to wait until Halloween :-) But I'm glad you didn't, since this is a nice answer. | |
| Oct 16, 2013 at 22:46 | history | edited | David E Speyer | CC BY-SA 3.0 |
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| Oct 16, 2013 at 19:32 | history | answered | David E Speyer | CC BY-SA 3.0 |