Timeline for Tate uniformization of nonsplit semistable elliptic curves
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2009 at 14:01 | comment | added | Jay |
I'll give this answer the credit because of the explicit citation, but really both this and Scott's were helpful. The better approach than what I wrote above is to take the entire S.E.S. 0 \to Z \to G_m \to E' \to 0 and twist it by K/Q_p (avoiding the extension+restriction of scalars) to get 0 \to Z' \to G_m' \to E \to 0. (Twisting of Z,G_m is done exactly as it is for E.) Taking Galois cohomology and computing, one gets` 0 \to G_m'(Q_p) \to E(Q_p) \to Z/2 \to 0, and if one wants to know E(Q_p)` one is left with explicitly describing G_m'(Q_p), e.g. via the kernel of the norm
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| Nov 4, 2009 at 3:48 | vote | accept | Jay | ||
| Nov 3, 2009 at 18:55 | comment | added | Jay | Thanks for the reference. I'd love to see Silverman's statement presented as a presentation of analytic groups, though. Any thoughts on that? (BTW, re: the possible index 2, see Scott Carnahan's comment about Galois cohomology.) | |
| Nov 3, 2009 at 18:32 | history | answered | moonface | CC BY-SA 2.5 |