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On number fields with given ramification

Part of: Algebraic number theory: global fields Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 November 2007

Gaëtan Chenevier
Gaëtan Chenevier*
Affiliation:
Institut Galilée LAGA, Université Paris 13, 99 Avenue J-B. Clément, 93430 Villetaneuse, France (email: chenevie@math.univ-paris13.fr, Gaetan.Chenevier@ens.fr)
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Abstract

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Let E be a CM number field and let S be a finite set of primes of E containing the primes dividing a given prime number l and another prime u split above the maximal totally real subfield of E. If ES denotes a maximal algebraic extension of E which is unramified outside S, we show that the natural maps are injective. We discuss generalizations of this result.

Keywords

global Galois groupsrestricted ramificationautomorphic forms

MSC classification

Secondary: 11F55: Other groups and their modular and automorphic forms (several variables) 11F80: Galois representations 11R32: Galois theory
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 6 , November 2007 , pp. 1359 - 1373
Copyright
Copyright © Foundation Compositio Mathematica 2007

References

The author is supported by the C.N.R.S.