An asymptotic formula for Tate–Shafarevich groups of CM elliptic curves at supersingular primes

Abstract Let K be an imaginary quadratic field, and let $E/\mathbb {Q}$ be an elliptic curve with complex multiplication by $\mathcal {O}_K$ . Let $K_\infty /K$ be the anticyclotomic $\mathbb {Z}_p$ -extension of K and $K_n$ be the intermediate layers. Under additional assumptions on Kobayashi’s signed Selmer groups, we prove an asymptotic formula for .