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On Jannsen’s conjecture for Hecke characters of imaginary quadratic fields
Bars Cortina, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data: 2007
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Jannsen conjecture ; Hecke motives ; Regularity
Publicat a: Publicacions matemàtiques, Vol. Extra (2007) , p. 29-42, ISSN 2014-4350

DOI: 10.5565/PUBLMAT_PJTN05_02

14 p, 184.2 KB

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