2011/03/24 by Tom Barnet-Lamb, David Geraghty, Michael Harris +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Calabi–Yau manifold #Mathematics #Pure mathematics
paper · pdf · doi:10.2977/prims/31
openalex publication_date 2011/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.)