A Family of Calabi-Yau Varieties and Potential Automorphy II

作者：Barnet Lamb Tom^*; Geraghty David; Harris Michael; Taylor Richard

来源：Publications of the Research Institute for Mathematical Sciences, 2011, 47(1): 29-98.

DOI：10.2977/PRIMS/31

• automorphic representation
• Calois representation
• Dwork family
• Sato-Tate conjecture

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.)

• 出版日期2011-3