Abstract
Let $F$ be a CM number field. We prove modularity lifting theorems for regular $n$-dimensional Galois representations over $F$ without any self-duality condition. We deduce that all elliptic curves $E$ over $F$ are potentially modular, and furthermore satisfy the Sato--Tate conjecture. As an application of a different sort, we also prove the Ramanujan Conjecture for weight zero cuspidal automorphic representations for $\mathrm{GL}_2(\mathbb{A}_F)$.
Citation
Patrick Allen. Frank Calegari. Ana Caraiani. Toby Gee. David Helm. Bao Le Hung. James Newton. Peter Scholze. Richard Taylor. Jack Thorne. "Potential automorphy over CM fields." Ann. of Math. (2) 197 (3) 897 - 1113, May 2023. https://doi.org/10.4007/annals.2023.197.3.2
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