Potential automorphy over CM fields

By P. Allen, Frank Calegari, Ana Caraiani, T. Gee, David Helm, B. Hung, James Newton, Peter Scholze, Richard Taylor, J. Thorne. Annals of Mathematics, 2018

63 citations recorded by the source corpus.

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 $\mathrm{GL}_2(\mathbf{A}_F)$.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/930e1a6d2340ab236e48afee30dbbad91cba73c2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Frank Calegari
2. T. Gee
3. Ana Caraiani
4. V. Pilloni
5. Peter Scholze
6. Lue Pan
7. M. Emerton
8. David Savitt

In Geometry and Topology

1. T. Gee
2. Peter Scholze
3. Frank Calegari
4. Ana Caraiani
5. V. Pilloni
6. G. Boxer
7. J. Thorne
8. David Geraghty

In Mathematical Physics

1. T. Gee
2. Peter Scholze
3. Frank Calegari
4. Ana Caraiani
5. V. Pilloni
6. G. Boxer
7. J. Thorne
8. David Geraghty

Citations in the corpus

• On the generic part of the cohomology of non-compact unitary Shimura varieties (2019, methodology): “This has been taken up in [ACC18], where the main result of the present paper is used to obtain local-global compatibility in the ordinary and (many) Fontaine–Laffaille cases.”
• Abelian surfaces over totally real fields are potentially modular (2018, methodology): “When K/F is totally imaginary, however, the result was only recently proved in [ACC18].”