a1 Institut Galilée LAGA, Université Paris 13, 99 Avenue J-B. Clément, 93430 Villetaneuse, France (email: email@example.com, Gaetan.Chenevier@ens.fr)
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.
(Received March 12 2007)
(Accepted May 21 2007)
(Online publication November 09 2007)
2000 Mathematics subject classification
The author is supported by the C.N.R.S.