On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.

Título inglés On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.
Título español Sobre la conjetura de Janssen para los caracteres de Hecke de campos cuadráticos imaginarios.
Autor/es Bars, Francesc
Organización Dep. Mat. Univ. Autòn. Barcelona, Bellaterra (Barcelona), España
Revista 0214-1493
Publicación 2007, Extra: 29-42, 18 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés We present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic field K of class number 1.
The conjecture is easy to check for Galois groups purely of local type (Section 1). In Section 2 we define the p-adic realizations associated to Hecke characters over K. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field K at p, which is related to the property that a global Galois group is purely of local type. Without this regularity assumption at p, we present a review of the known situations in the critical case (Section 3) and in the non-critical case (Section 4) for these realizations. We relate the conjecture to the non-vanishing of some concrete non-critical values of the associated p-adic L-function of the Hecke character.
Finally, in Section 5 we prove that the conjecture follows from a general conjecture on Iwasawa theory for almost all Tate twists.

[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
Clasificación UNESCO 120500
Palabras clave español Teoría de números ; Funciones L ; Grupo de Galois ; Teoría de Iwasawa
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