Timeline for On injectivity of Galois representation
Current License: CC BY-SA 3.0
6 events
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May 27, 2011 at 8:05 | comment | added | Kevin Buzzard | @gummi: there is a number field, Galois over the rationals, with $Gal(M/Q)$ isomorphic to the monster group. Why not try and prove that this group cannot possibly show up in any number field obtained by adjoining $n$-torsion points of elliptic curves over the rationals. | |
May 26, 2011 at 16:43 | comment | added | SGP | @gummi: the result of Serre that the image of Galois on the Tate module of abelian varieties is as large as possible (if the dimension $g$ is odd, then the image is open in $Sp_{2g}(Z_l)$) suggests that the answer is negative. | |
May 26, 2011 at 16:14 | comment | added | François Brunault | @gummi : My impression is that the absolute Galois group is too complicated an object to be contained in a group like $\operatorname{GL}_2(\widehat{\mathbf{Z}})^{\mathbf{N}}$, but I don't have an argument right now. | |
May 26, 2011 at 16:00 | comment | added | gummi | what if we consider the product of the $l$-adic representations for all primes $l$ and all elliptic curves over $Q$? | |
May 26, 2011 at 15:57 | vote | accept | gummi | ||
May 26, 2011 at 15:50 | history | answered | François Brunault | CC BY-SA 3.0 |