Timeline for Books on reductive groups using scheme theory
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 11, 2010 at 5:14 | comment | added | JS Milne | @Brian: I agree that if you try to directly transfer the proof in the smooth case to the nonsmooth case, you can sometimes run into some very heavy scheme theory, but there are also elementary proofs using Hopf algebras. I learnt this from Waterhouse's book. As Serre pointed out, Hopf algebra proofs don't illuminate, but my strategy is to sketch the geometric argument and write out the Hopf algebra argument (when necessary). I'm only doing things over fields (or rings, when it's just as easy). | |
| Mar 11, 2010 at 4:35 | comment | added | Anonymous | Straight from the author's website: May 2010. New version of Algebraic Groups, Lie Groups, and their Arithmetic Subgroups | |
| Mar 11, 2010 at 4:34 | comment | added | BCnrd | @Jim: When learning these things on my own, the only way I could make scheme-theoretic versions of the proofs of various things was to use what I knew from EGA, descent theory, etc.. So my impression was that without a certain amount of "post-Hartshorne" algebraic geometry technique already known, an attempt to do this stuff scheme-theoretically in a clean way would fail. I'd be happy to be proved wrong! Or even better, for there to be an alg. gps. book that, like with "Neron Models", develops the necessary techniques and then applies it to do interesting things. | |
| Mar 11, 2010 at 1:37 | vote | accept | Harry Gindi | ||
| Mar 11, 2010 at 1:30 | comment | added | Harry Gindi | Brilliant! Is there any way I can be "kept posted" on that book? | |
| Mar 11, 2010 at 1:15 | history | answered | JS Milne | CC BY-SA 2.5 |