Timeline for Quotient of a reductive group by a non-smooth subgroup
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| May 25, 2013 at 18:04 | answer | added | Jim Humphreys | timeline score: 3 | |
| Mar 28, 2013 at 15:14 | answer | added | anon | timeline score: 0 | |
| Mar 28, 2013 at 14:37 | comment | added | user29283 | "footnote 35" in the preceding comment refers to the new SMF edition. | |
| Mar 28, 2013 at 14:36 | comment | added | user29283 | For any group scheme $G$ of finite type over any field $k$ and any closed $k$-subgroup scheme $H$ of $G$, the fppf quotient sheaf $G/H$ is represented by a separated finite type $k$-scheme and the map $q:G \rightarrow G/H$ is faithfully flat (so $q$ inherits "any" property of $H \rightarrow {\rm{Spec}}(k)$ that is fppf-local on the base). In particular, if $G$ is smooth then $G/H$ is smooth. See SGA3, Exp. VI$_{\rm{A}}$, section 3 for the construction (doesn't use quasi-projective methods, but see footnote 35). For affineness when $G$ is affine and $H$ is normal, see VI$_{\rm{B}}$, 11.17. | |
| Mar 28, 2013 at 14:15 | history | asked | Mikhail Borovoi | CC BY-SA 3.0 |