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
6 events
| when toggle format | what | by | license | comment | |
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| Jun 21, 2019 at 12:44 | comment | added | Shreya | That actually clears up things a bit, thanks! | |
| Jun 20, 2019 at 14:53 | comment | added | Joe Silverman | @Mojojojo I haven't looked at Milne in a while, but I think one pretty much always has to do a height descent at some point in the argument. The proof of MW has two parts. First is "weak" Mordell-Weil, which is proving $E(K)/mE(K)$ is finite. That proof is cleaner if you know and use group cohomology, which is Milne's approach, and I do that in VIII Sec. 2; but I also do it more directly, essentially by unsorting the cohomology, in VIII Sec. 1. But Step 2, namely going from finiteness of $E(K)/m(K)$ to finite generation of $E(K)$, needs a height-type argument AFAIK. | |
| Jun 20, 2019 at 14:02 | vote | accept | Shreya | ||
| Jun 20, 2019 at 14:01 | comment | added | Shreya | Thanks for the answer! I have started going through RPEC but soon after finishing the proof of Mordell-Weil and digesting it well, I hope to be back to AEC or Milne. I do have background in both AG and ANT, so might go through the contents of both them roughly to decide which one will be best suitable for me. I suspect that AEC and Milne prove the same generalization of Mordell-Weil but have different approaches, that is, one with height descent argument and another using group cohomology, am I right | |
| Jun 19, 2019 at 19:33 | comment | added | Asvin | I found Milne's treatment of Mordell Weil really clear. | |
| Jun 19, 2019 at 19:09 | history | answered | Joe Silverman | CC BY-SA 4.0 |