Timeline for Over a finite field, does a torsor under the component group of G lift to a torsor under G?
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| Jun 29, 2014 at 23:29 | vote | accept | Question Mark | ||
| Jun 29, 2014 at 21:45 | comment | added | user27920 | Serre's Corollary 2 in 2.4 (as opposed to Corollary 3 which you mention) provides surjectivity in complete generality: for smooth groups of finite type (not just linear algebraic) over perfect fields with cohomological dimension $\le 1$. His proof of the main theorem from which the corollaries are deduced use Chevalley's theorem on the structure of the identity component beyond the affine case (over perfect fields) and the simple structure of connected unipotent groups over perfect fields. Throughout Chapter III it is tacitly assumed (as noted at the start) that the ground field is perfect. | |
| Jun 29, 2014 at 21:18 | history | answered | Daniel Loughran | CC BY-SA 3.0 |