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The Sato-Tate conjecture for Hilbert modular forms
The Sato-Tate conjecture for Hilbert modular forms
- Publication Year :
- 2009
-
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.<br />59 pages. Essentially final version, to appear in Journal of the AMS. This version does not incorporate any minor changes (e.g. typographical changes) made in proof
- Subjects :
- Pure mathematics
Conjecture
Mathematics - Number Theory
Applied Mathematics
General Mathematics
Mathematics::Number Theory
010102 general mathematics
Sato–Tate conjecture
Modular form
Automorphic form
11F33
Type (model theory)
Galois module
01 natural sciences
0103 physical sciences
FOS: Mathematics
Number Theory (math.NT)
010307 mathematical physics
0101 mathematics
Algebraic number
Argument (linguistics)
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....fa6785c146ed89a53bddadfb0f304f0a