Potential automorphy over CM fields - Allen, PB; Calegari, F; Caraiani, A; Gee, T; Helm, D; Le Hung, BV; Newton, J; Scholze, P; Taylor, R; Thorne, JA (Princeton University Press, 2023)
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 GL2(AF ).