Work

A Family of Calabi–Yau Varieties and Potential Automorphy II

Year: 2011

Type: article

Abstract: We prove new potential modularity theorems for n-dimensional essentially self-dual l -adic representations of the absolute Galois group of a totally real field. Most notably, in the ordinary case we prove quite a general result. Our results suffice to show that all the symmetric powers of any non-CM, holomorphic, cuspidal, elliptic modular newform of weight greater than one are potentially cuspidal automorphic. This in turns proves the Sato–Tate conjecture for such forms. (In passing we also note that the Sato–Tate conjecture can now be proved for any elliptic curve over a totally real field.)

Source: Publications of the Research Institute for Mathematical Sciences

DOI: 10.2977/prims/31

Authors: Tom Barnet-Lamb, David Geraghty, Michael Harris, Richard Taylor

Institutions: Centre National de la Recherche Scientifique, Harvard University, Institute for Advanced Study, Brandeis University, Institut de Mathématiques de Jussieu-Paris Rive Gauche

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: Galois Representations and Modular Forms