A family of Calabi-Yau varieties and potential automorphy

2010/03/25 by Michael Harris, Nick Shepherd-Barron, Richard Taylor · 7 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.4007/annals.2010.171.779

openalex publication_date 2010/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

Abstract

We prove potential modularity theorems for l-adic representations of any dimension. From these results we deduce the Sato-Tate conjecture for all elliptic curves with nonintegral j -invariant defined over a totally real field.

Citations

• Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques
• Ring-Theoretic Properties of Certain Hecke Algebras
• On Certain L-Functions
• Modular Elliptic Curves and Fermat's Last Theorem

Cited by

• -ADIC EISENSTEIN SERIES AND -FUNCTIONS OF CERTAIN CUSP FORMS ON DEFINITE UNITARY GROUPS
• Sato-Tate groups of genus 2 curves
• A Family of Calabi–Yau Varieties and Potential Automorphy II
• Sato-Tate groups of some weight 3 motives
• Even Galois representations and the Fontaine–Mazur conjecture
• Elliptic curve [wikipedia]
• Sato–Tate conjecture [wikipedia]

Related

• A Family of Calabi–Yau Varieties and Potential Automorphy II
• Potential automorphy over CM fields
• Modularity of Calabi--Yau varieties: 2011 and beyond
• The Sato-Tate conjecture for Hilbert modular forms
• Modularity of Calabi-Yau varieties