The Arithmetic of Elliptic Curves
《The Arithmetic of Elliptic Curves》 · 第 332 页 · Chapter X，Section 4「The Selmer and Shafarevich–Tate Groups」，Definition
The Shafarevich–Tate group of $E/K$ is the subgroup of $WC(E/K)$ defined by $\Sha(E/K)=\ker\bigl(WC(E/K)\to\prod_{v\in M_K}WC(E/K_v)\bigr)$.