Timeline for Can someone suggest a path to study Mordell-Weil theorem for someone studying on their own?
Current License: CC BY-SA 4.0
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| Jun 20, 2019 at 14:12 | comment | added | anon | Everyone should read Cassels's historical essay on the genesis of Mordell's theorem (Math. Proc. Cambridge Philos. Soc 1983), and no one should try to learn the theorem by reading Mordell's original 1922 paper. | |
| Jun 20, 2019 at 14:04 | comment | added | Shreya | Thank you for posting the link to your notes! I have started going through $E/\mathbb{Q} $ with a rational 2-torsion point case using Rational Points on Elliptic Curves, have heard some praises about Cassels as well, so I think I might check out your notes as well since they cover the same contents. | |
| Jun 19, 2019 at 20:39 | comment | added | Noam D. Elkies | That's also the historical path. Once you understand how to do it when there's a 2-torsion point (which is a natural generalization of Fermat's original "descent"), and how to generalize to arbitrary number fields (which is a common theme in modern number theory), you automatically get to drop the 2-torsion assumption, because you always have a 2-torsion point over some number field. The group structure (which was obtained relatively late, by Mordell) also explains the apparent miracle that two "descents" get you back to the original curve. | |
| Jun 19, 2019 at 20:25 | history | answered | Martin Bright | CC BY-SA 4.0 |