Timeline for If $E(K)=E(L)$ for an elliptic curve $E$ and an algebraic extension $L/K$, what can we say about $Sel(E/K), Sel(E/L), L/K$?
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| Mar 3, 2015 at 20:03 | comment | added | Chris Wuthrich | I assume that Sel$(E/K)$ is the group that fits into a short exact sequence between $E(K)$ and Sha$(E/K)$. Otherwise you need to fix your $n$ in $n$-Selmer group (or your isogeny). So your question is equivalent to asking about the growth of the Tate-Shafarevich group in the tower. Basically anything can happen. Iwasaw theory gives examples of exploding growth as well as frequent stabilisation. | |
| Mar 3, 2015 at 18:50 | history | edited | Donggeon Yhee | CC BY-SA 3.0 |
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| Mar 3, 2015 at 18:40 | review | First posts | |||
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| Mar 3, 2015 at 18:35 | history | asked | Donggeon Yhee | CC BY-SA 3.0 |