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)].
@article{urn:eudml:doc:41913,
title = {On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.},
journal = {Publicacions Matem\`atiques},
year = {2007},
pages = {29-42},
zbl = {1183.11070},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41913}
}
Bars, Francesc. On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.. Publicacions Matemàtiques, (2007), pp. 29-42. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41913/