Title: The Sato-Tate conjecture for Hilbert modular forms
Abstract: We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal automorphic representations of $\GL_2(\A_F)$, $F$ a totally real field, which are not of CM type. The argument is based on the potential automorphy techniques developed by Taylor et. al., but makes use of automorphy lifting theorems over ramified fields, together with a 'topological' argument with local deformation rings. In particular, we give a new proof of the conjecture for modular forms, which does not make use of potential automorphy theorems for non-ordinary $n$-dimensional Galois representations.
Publication Year: 2009
Publication Date: 2009-12-05
Language: en
Type: preprint
Access and Citation
Cited By Count: 2
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot