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