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

摘要

Let p >= 5 be a prime number and E/Q an elliptic curve with good supersingular reduction at p. Under the generalized Heegner hypothesis, we investigate the p-primary subgroups of the Tate-Shafarevich groups of E over number fields contained inside the anticyclotomic Z(p)-extension of an imaginary quadratic field where p splits.

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