Timeline for Rational points techniques on curves not using their Jacobian
Current License: CC BY-SA 3.0
4 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 25, 2014 at 22:17 | comment | added | Ariyan Javanpeykar | @DamianRössler Yes, you are right. Note that there are some other papers on his website in which he and others apply these methods to other curves. I didn't realize the OP was asking for effective techniques and probably only read his "I want to know if there are also techniques for studying $C(K)$ that don't use the Jacobian". (Quite interestingly: somethin special to Kim's approach is that it shows that these classical finiteness statements (proven by Siegel) are related to other conjectures like the Fontaine-Mazur conjecture.) | |
| Aug 25, 2014 at 21:25 | comment | added | Damian Rössler | The method of Kim is very interesting but he can only prove Siegel's theorem for the projective line, as far I can see. In that case, (much) more elementary proofs can be made quite effective (see Silverman's book on elliptic curves) but even this does not give a method to find all the rational points on a curve. | |
| Aug 25, 2014 at 19:42 | history | answered | Ariyan Javanpeykar | CC BY-SA 3.0 |