Timeline for Can you get Siegel's theorem "for free" from modularity and Mazur's Eisenstein Ideal paper?
Current License: CC BY-SA 2.5
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Sep 23, 2010 at 17:48 | comment | added | James Weigandt | Ha! I feel silly. This is question is essentially Remark 6.5 in on page 295 of Silverman's AEC (2nd Edition). | |
| Aug 31, 2010 at 11:04 | comment | added | Felipe Voloch | Faltings work doesn't use transcendence or dioph approximation and you can deduce Siegel's thm from the Mordell conjecture. | |
| Aug 31, 2010 at 5:50 | history | edited | Franz Lemmermeyer | CC BY-SA 2.5 |
fixed a typo
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| Aug 31, 2010 at 5:06 | comment | added | James Weigandt | Cool! Thanks Brian. I definitely learned something. I can see now that my question sort of springs from a great ignorance of the work of Faltings. | |
| Aug 31, 2010 at 4:30 | comment | added | BCnrd | You mean to refer to "Rat'l isogenies of prime degree". The Eisenstein paper addresses isogenies whose kernel is constant (i.e., all pts are rat'l). Siegel's thm is irrelevant in Mazur's work. Anyway, your argument seems circular: the "modularity thm" relates (certain) eigenforms to $\ell$-adic Galois representations, and to know an isogeny class of elliptic curves is captured by Galois rep'n one needs Tate's isogeny conjecture for elliptic curves...first proved in general for elliptic curves over # fields by Faltings when he proved it in all dim's...via his proof of Shaf. conj. in all dim! | |
| Aug 31, 2010 at 3:18 | history | asked | James Weigandt | CC BY-SA 2.5 |