Timeline for Why $G\to G/H$ is faithfully flat?
Current License: CC BY-SA 3.0
6 events
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| Jul 25, 2012 at 2:03 | comment | added | Jia-jun Ma | Here raise a question: if $G/H$ is quasi-affine, is $G/H$ locally trivial? | |
| Jul 25, 2012 at 2:03 | comment | added | Jia-jun Ma | Thank you very much for your answer! I have find a English book with a proof of faithfully flat: Section 5.7 in Jantzen's Representations of algebraic groups. For the locally trivial part. Yes, I means Zariski locally trivial as you said. I guess I may not be true in general. But it is quite interesting that although this is not true, by the faithfully flatness, the vector bundle $G\times_H V\to G/H$ is locally trivial, c.f. Secion~5.9 of Jantzen's book, where $V$ is a finite dimensional (over $k$) representation of $H$. | |
| Jul 25, 2012 at 1:53 | vote | accept | Jia-jun Ma | ||
| Jul 24, 2012 at 13:23 | history | edited | Baptiste Calmès | CC BY-SA 3.0 |
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| Jul 24, 2012 at 12:41 | history | edited | Baptiste Calmès | CC BY-SA 3.0 |
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| Jul 24, 2012 at 12:23 | history | answered | Baptiste Calmès | CC BY-SA 3.0 |