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Let $p\ge 5$ be a prime number and $E/\mathbf{Q}$ an elliptic curve with goodsupersingular reduction at $p$. Under the generalized Heegner hypothesis, weinvestigate the $p$-primary subgroups of the Tate--Shafarevich groups of $E$over number fields contained inside the anticyclotomic $\mathbf{Z}_p$-extensionof an imaginary quadratic field where $p$ splits.

Asymptotic formula for Tate-Shafarevich groups of $p$-supersingular elliptic curves over anticyclotomic extensions