Potential automorphy over CM fields

doi:10.4007/annals.2023.197.3.2

Potential automorphy over CM fields

2023-05-01

15

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AI

DOI：10.4007/annals.2023.197.3.2

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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 mod-ular, 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).

Keyword:

Galois representations

automorphic forms

Potential automorphy over CM fields

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