Timeline for Comparing algebraic group orbits over big and small algebraically closed fields
Current License: CC BY-SA 4.0
7 events
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| Mar 9, 2022 at 12:17 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
a minor typo
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| Dec 21, 2010 at 6:16 | comment | added | BCnrd | So to continue my comment above, we have removed the scheme-theoretic apparatus in the end. However, certain ways of thinking which inspire the argument are very natural from the scheme viewpoint, and may be less likely to jump out of the page from a more classical viewpoint (even if we succeed to express the final argument in entirely classical terms, as we have just seen we can do). | |
| Dec 21, 2010 at 6:08 | comment | added | BCnrd | Schemes can be avoided. First, G, X, and S can be viewed as varieties. The transporter $T_{x,x′}$ is a scheme-theoretic pullback of closed subvariety under a morphism, but could use its underlying variety (classical preimage of Zariski-closed set); fibers over geometric pts of S (inside G viewed over the corresponding alg. closed field) still have the "expected" geometric pts. And Chevalley is overkill: just need that if a map $Y\rightarrow Z$ of affine k-varieties with irreducible Z localizes to empty over k(Z), then factors through a proper closed subvariety, which is elementary | |
| Dec 20, 2010 at 16:14 | comment | added | Jim Humphreys | This scheme viewpoint looks natural, though of course it's always a problem to combine it with the limited goals of many papers that deal with fairly concrete questions about linear groups, etc. My own scheme involvement has been sparse, so I have to ponder your answer further. | |
| Dec 19, 2010 at 21:12 | history | edited | BCnrd | CC BY-SA 2.5 |
edited body
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| Dec 19, 2010 at 19:43 | history | edited | BCnrd | CC BY-SA 2.5 |
added 978 characters in body
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| Dec 19, 2010 at 18:58 | history | answered | BCnrd | CC BY-SA 2.5 |