Timeline for Over which fields does the Mordell-Weil theorem hold?
Current License: CC BY-SA 3.0
5 events
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| Oct 1, 2012 at 22:16 | comment | added | Felipe Voloch | @François: The first field that you suggest has been used by Ulmer to construct elliptic curves with arbitrary large rank over function fields, using that $k(T^{1/n})$ are all abstractly the same field, so that won't work. Don't know about the second one. | |
| Oct 1, 2012 at 21:12 | comment | added | François Brunault | Thanks for your answer. I don't know if the following would work, but what happens with the simpler case $K=\cup_n k(T^{1/n})$? Or to mimick the situation in Mazur's conjecture, one could try to take an inverse system of multiplication-by-$n$ maps on a given elliptic curve $E/k$. | |
| Oct 1, 2012 at 19:27 | history | edited | Felipe Voloch | CC BY-SA 3.0 |
added 138 characters in body
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| Oct 1, 2012 at 19:14 | comment | added | Will Sawin | $A$ is a variety over $K$, not a variety over $k$. $Jac(C_n)$ is a variety over $k$. Why should they be the same? | |
| Oct 1, 2012 at 14:35 | history | answered | Felipe Voloch | CC BY-SA 3.0 |