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

Publicacions Matemàtiques (2007)

- Volume: 51, Issue: Extra, page 29-42
- ISSN: 0214-1493

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topBars, 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 -

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