Elliptic curves over $\mathbb{Q}_\infty$ are modular

Elliptic curves over $Q_{\infty}$ are modular

$Elliptic curves over $\mathbb{Q}_\infty$ are modular cover$

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We show that if $p$ is a prime, then all elliptic curves defined over the cyclotomic $Z_{p}$ -extension of $Q$ are modular.

Jack A. Thorne, Elliptic curves over $Q_{\infty}$ are modular. J. Eur. Math. Soc. 21 (2019), no. 7, pp. 1943–1948