Timeline for Is a quotient of a reductive group reductive?
Current License: CC BY-SA 2.5
4 events
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| Mar 28, 2010 at 17:25 | comment | added | Wilberd van der Kallen | Of course Brian Conrad is right that invoking Haboush's theorem is like killing a fly with a sledgehammer. But I like this particular use of a sledgehammer. It reduces the problem to one where one can argue as in the characteristic zero case. It makes one feel the result is true for a reason. | |
| Mar 28, 2010 at 14:37 | comment | added | Wilberd van der Kallen | Geometrically reductive means that if G acts algebraically on an algebra A and I is an invariant ideal, then any element of A/I that is fixed by G has a power that lifts to an element of A that is fixed by G. There are other formulations. It is now easy to see that a quotient of a geometrically reductive G is geometrically reductive. One does not need Haboush's theorem, which is much deeper. | |
| Oct 2, 2009 at 4:11 | comment | added | Anton Geraschenko | What does "geometrically reductive" mean? | |
| Oct 2, 2009 at 3:49 | history | answered | Jarod Alper | CC BY-SA 2.5 |