Timeline for Galois Action on the lines in the k^{2}_{E}
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| May 19, 2012 at 18:39 | vote | accept | Dragon | ||
| Oct 23, 2010 at 11:59 | answer | added | S. Carnahan♦ | timeline score: 2 | |
| Oct 15, 2010 at 13:05 | comment | added | Dragon | Still waiting an answer or any notes | |
| Oct 12, 2010 at 11:14 | history | edited | Dragon | CC BY-SA 2.5 |
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| Oct 11, 2010 at 12:35 | history | edited | Cam McLeman |
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| Oct 11, 2010 at 12:15 | history | edited | Dragon | CC BY-SA 2.5 |
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| Oct 11, 2010 at 12:09 | history | edited | Dragon | CC BY-SA 2.5 |
added 11 characters in body; added 19 characters in body; edited body; edited body
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| Oct 10, 2010 at 5:28 | history | edited | Bjørn Kjos-Hanssen |
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| Oct 8, 2010 at 13:06 | comment | added | Dragon | Sorry for confusing, theres no isomorphism between E points of the projective line and the tree of SL(2,E). Scott, you are right and my main questions were: 1-How to determine adjacent lattices given V, dimV=2 over E? 2-How Gal(E/F) acting on these adjacent lattices? i might was thinking | |
| Oct 7, 2010 at 3:19 | comment | added | S. Carnahan♦ | The tree of $SL(2,E)$ has vertices given by homothety classes of lattices, and edges given by lattice inclusions with quotient isomorphic to $k_E$. This is not isomorphic to the $E$ points of the projective line, and it does not parametrize lines in $k^2_E$. The $E$ points of the projective line are identified with the ends of the tree, and the lines in $k^2_E$ can be identified with the adjacent points of a fixed lattice defined over $\mathcal{O}_F$. | |
| Oct 7, 2010 at 3:17 | comment | added | Chandan Singh Dalawat | I don't know if this special case helps : Assume that the residue field k of F is finite with q=p^f elements, and that the degree d=[l:k] of the residue field l of E over k divides q-1. Then the normal basis theorem implies that for every character x:Gal(l|k)-->k^*, the x-eigenspace l(x) is a k-line. | |
| Oct 7, 2010 at 2:54 | comment | added | S. Carnahan♦ | I tried to fix your LaTeX in a way that preserved the meaning of what you wrote, but there are some factual errors in your question. | |
| Oct 7, 2010 at 2:50 | history | edited | S. Carnahan♦ | CC BY-SA 2.5 |
LaTeX repair
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| Oct 6, 2010 at 17:41 | comment | added | Dragon | am working on base change for Gl(2), and this mean if i have 2 trees, one for GL(2,F) and another for GL(2,E) where E is the extension of F. So I Should describ the base change over these trees. | |
| Oct 6, 2010 at 16:48 | comment | added | Chandan Singh Dalawat | Perhaps you should explain the notation ? | |
| Oct 6, 2010 at 16:30 | history | asked | Dragon | CC BY-SA 2.5 |