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

### Antonio Lei (Universite Laval)

Thu Mar 17, 22:00-23:00 (6 months ago)

Abstract: Let $p\ge 5$ be a prime number and $E/\mathbf{Q}$ 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 $\mathbf{Z}_p$-extension of an imaginary quadratic field where $p$ splits. This is joint work with Meng Fai Lim and Katharina Mueller.

number theory

Audience: researchers in the topic

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