Timeline for Tate–Shafarevich group and $\sigma \phi(C)=-\phi \sigma(C)$ for all $C \in \operatorname{Sha}(E/L)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 4 at 9:08 | comment | added | Chris Wuthrich | It is the usual action of the quotient $G/H$ on $H^i(H,M)$ when $H$ is normal in $G$. To check that this is the same action as defined on $WC$ sounds like a good exercise to do. Be careful to view elements in the Weil-Chatelet groups as torsors, not just as curves. | |
| Jan 4 at 4:39 | comment | added | Duality | Thank you very much. I would like to extend my sincere New Year greetings to you. The action $*$ you defined seems unfamiliar to me. Where does your action $*$ originate from? Does it commute with the action on $WC(E/L)$? To clarify, if we denote $\tau: WC(E/L) \cong H^1(G_L, E)$, and take $[C/L] \in WC(E/L)$, does $\tau([\sigma C/L])) = \phi_*(\tau([C/L]))$? | |
| Dec 30, 2023 at 14:09 | vote | accept | Duality | ||
| Dec 29, 2023 at 23:50 | history | edited | LSpice | CC BY-SA 4.0 |
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| Dec 29, 2023 at 23:24 | history | answered | Chris Wuthrich | CC BY-SA 4.0 |