Timeline for How Galois group acts on Tate-Shafarevich group?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2023 at 17:42 | comment | added | Duality | Thank you very much, if $φ: E×C\to C, (P,p)\to φ(P,p)$, you explains, $φ^{\sigma}: E×C^{\sigma}\to C^{\sigma}, (P,p) \to φ^{\sigma}(P,p)$ gives the action of $E$ to $C^{\sigma}$. Indeed, this is defined over $K$ because it is Galois invariant under the action of $Gal(L/K)$ ! Could you please tell me why the $φ(P,p)$ is polynomial ? | |
| Jun 7, 2023 at 16:34 | comment | added | Will Sawin | This action should only exist if $E$ itself is defined over $K$. In that case, one can simply apply $\sigma$ to the coefficients of polynomial equations defining the action of $E$ on $C$. | |
| Jun 7, 2023 at 14:51 | history | edited | R.P. | CC BY-SA 4.0 |
added 128 characters in body
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| Jun 7, 2023 at 14:47 | history | asked | Duality | CC BY-SA 4.0 |