Timeline for Frobenius kernel for unipotent algebraic groups
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2013 at 17:33 | comment | added | Xingting | Yes, I'm interested in non-smooth ones. Thanks for the reference you gave. | |
| Feb 16, 2013 at 8:49 | comment | added | user30379 | I suppose $G$ is meant to be affine (otherwise a supersingular elliptic curve would be a counterexample). We can assume the ground field is algebraically closed, and then the smooth connected subgroup $G_{\rm{red}}$ inherits the hypothesis, so it contains no nontrivial torus. Consequently, $G_{\rm{red}}$ must be unipotent, by the structure theory of smooth connected affine groups over alg. closed fields. Are you interested in non-smooth $G$? If so then 4.3.1 in Exp. XVII of SGA3 gives the affirmative answer (absence of $\mu_p$ forces unipotence as a group scheme, assuming connectedness). | |
| Feb 16, 2013 at 2:28 | comment | added | Xingting | I forgot to say $G$ is connected. | |
| Feb 16, 2013 at 2:28 | history | edited | Xingting | CC BY-SA 3.0 |
added 9 characters in body; added 4 characters in body
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| Feb 15, 2013 at 23:08 | comment | added | user30035 | What about if $G$ is etale of order prime to $p$? | |
| Feb 15, 2013 at 20:02 | history | asked | Xingting | CC BY-SA 3.0 |