I' m looking for a proof of the fact that the Hasse local-global principle holds for every homogeneous space of elliptic curve $E $ defined over $\Bbb Q$ if and only if the Tate-Shafarevich group of $E$ is trivial.
I'm wondering why 山（E/$\Bbb Q$）is characterized as the group of everywhere local trivial homogeneous space for $\Bbb Q$.
Any referrences (webpage, book, etc...) are also appreciated. Thank you.