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

### Jack A. Thorne

University of Cambridge, UK

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## Abstract

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

## Cite this article

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

DOI 10.4171/JEMS/877