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arXiv · 2504.05734

An Asymptotic formula for Tate-Shafarevich groups of CM elliptic curves at supersingular primes

Katharina Müller
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Abstract

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

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Katharina Müller. 2025-04-08. An Asymptotic formula for Tate-Shafarevich groups of CM elliptic curves at supersingular primes. https://arxiv.org/abs/2504.05734

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