Timeline for Zariski-closed subsemigroups of SL_n(C) are groups
Current License: CC BY-SA 2.5
11 events
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| Nov 22, 2010 at 18:43 | comment | added | Jim Humphreys | @darij: It's a question of using older language about varieties, with the ground field being arbitrary (but infinite). The function algebras certainly play a leading role, especially in Hochschild's Springer graduate text following Chevalley's 1955 book. Much of this works well enough in char 0, but otherwise gets out of control when you construct quotients, etc. Chevalley's version of algebraic geometry was a step toward what is now standard (and may have helped speed the transition). My education however started out with Weil's book ;-( | |
| Nov 22, 2010 at 17:53 | comment | added | darij grinberg | What exactly is the Chevalley viewpoint? Considering algebraic groups as varieties rather than schemes? Or working with algebraic groups through their Hopf algebras? | |
| Nov 22, 2010 at 17:52 | comment | added | Jim Humphreys | P.S. Tag added. | |
| Nov 22, 2010 at 17:51 | history | edited | Jim Humphreys |
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| Nov 22, 2010 at 13:57 | comment | added | Jim Humphreys |
Note that the linked paper relies on the older Chevalley viewpoint about algebraic groups and algebraic geometry over arbitrary fields, which Hochschild also followed much later on. This doesn't work well in prime characteristic, so eventually the framework used by Chevalley and others shifted (and schemes came in). But for a field like $\mathbb{C}$ none of that really affects the question here.
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| Nov 22, 2010 at 13:09 | vote | accept | Colin McQuillan | ||
| Nov 22, 2010 at 12:56 | vote | accept | Colin McQuillan | ||
| Nov 22, 2010 at 13:00 | |||||
| Nov 22, 2010 at 12:51 | answer | added | darij grinberg | timeline score: 3 | |
| Nov 22, 2010 at 12:50 | answer | added | Keivan Karai | timeline score: 24 | |
| Nov 22, 2010 at 12:30 | answer | added | Andreas Thom | timeline score: 1 | |
| Nov 22, 2010 at 11:33 | history | asked | Colin McQuillan | CC BY-SA 2.5 |