Timeline for When is an orbit spherical?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
|
|
| Sep 9, 2012 at 20:52 | vote | accept | Jesko Hüttenhain | ||
| Sep 8, 2012 at 12:40 | comment | added | Jesko Hüttenhain | @Jim: Good idea, I added it. | |
| Sep 8, 2012 at 12:39 | history | edited | Jesko Hüttenhain |
edited tags
|
|
| Sep 8, 2012 at 11:33 | comment | added | Jim Humphreys | @grp: Sorry for the clumsy wording. Richardson's main point was to rewrite the analytic proof in algebraic language via Grothendieck; he could then incorporate char p as well, using Haboush's theorem (reductive implies geometrically reductive). That affirmed Nagata's earlier approach based on assuming Mumford's conjecture. But the question here is just about char 0. In their 1977 paper (Math. Ann. 230), CPS gave a broader treatment in char p, showing how induction functors come into the picture.. | |
| Sep 8, 2012 at 5:47 | comment | added | grp | @Jim Humphreys: I think that what I wrote was accurate: in Theorem A of Richardson's paper "Affine coset spaces of reductive algebraic groups" in Bulletin of the LMS 9 (1977), pp. 38--41, he uses Haboush's theorem (Mumford's conjecture) to prove the result in arbitrary characteristic. He states explicitly early in the paper that his purpose is to record a proof valid in any characteristic. I'm not sure which papers of Richardson and C-P-S you have in mind, but please look at the Richardson paper I have just mentioned. | |
| Sep 7, 2012 at 22:02 | comment | added | Jim Humphreys | @Jesko: Maybe an added tag algebraic-groups would be appropriate? | |
| Sep 7, 2012 at 22:01 | comment | added | Jim Humphreys | @grp: Actually, Richardson's work is in characteristic 0 but based more on Grothendieck's algebraic geometry, whereas the work of Haboush was aimed at prime characteristic where Mumford's conjecture was then open. (A paper by Cline-Parshall-Scott extended the results on affine quotients to prime characteristic.) | |
| Sep 7, 2012 at 21:59 | answer | added | Jim Humphreys | timeline score: 4 | |
| Sep 7, 2012 at 11:59 | comment | added | grp | @Jesko: I think your affineness condition on the orbit $G/H$ is equivalent to your hypothesis that the underlying reduced scheme of the identity component $H^0$ is reductive. This equivalence is a theorem of Borel & Harish-Chandra in characteristic 0 (proved via topological methods over $\mathbf{C}$), Richardson in any characteristic (proved via Haboush's work on Mumford's conjecture in GIT), and finally proved by Borel in any characteristic via etale cohomology (adapting the argument with H-C). | |
| Sep 7, 2012 at 11:47 | history | edited | Jesko Hüttenhain | CC BY-SA 3.0 |
added 76 characters in body
|
| Sep 7, 2012 at 10:16 | answer | added | Dave Anderson | timeline score: 7 | |
| Sep 7, 2012 at 9:03 | history | asked | Jesko Hüttenhain | CC BY-SA 3.0 |