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

Bars, Francesc. "On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.." Publicacions Matemàtiques 51.Extra (2007): 29-42. <http://eudml.org/doc/41913>.

@article{Bars2007,
abstract = {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)].},
author = {Bars, Francesc},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de números; Funciones L; Grupo de Galois; Teoría de Iwasawa; Jannsen conjecture; Hecke motives; regularity},
language = {eng},
number = {Extra},
pages = {29-42},
title = {On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.},
url = {http://eudml.org/doc/41913},
volume = {51},
year = {2007},
}

TY - JOUR
AU - Bars, Francesc
TI - On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.
JO - Publicacions Matemàtiques
PY - 2007
VL - 51
IS - Extra
SP - 29
EP - 42
AB - 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)].
LA - eng
KW - Teoría de números; Funciones L; Grupo de Galois; Teoría de Iwasawa; Jannsen conjecture; Hecke motives; regularity
UR - http://eudml.org/doc/41913
ER -