Potential automorphy over CM fields

Patrick B. Allen*, Frank Calegari, Ana Caraiani, Toby Gee, David Helm, Bao V. Le Hung, James Newton, Peter Scholze, Richard Taylor, Jack A. Thorne

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 diffierent sort, we also prove the Ramanujan Conjecture for weight zero cuspidal automorphic representations for GL2(AF ).

Original languageEnglish (US)
Pages (from-to)897-1113
Number of pages217
JournalAnnals of Mathematics
Issue number3
StatePublished - 2023


  • Galois representations
  • automorphic

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this