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Archiv der Mathematik

, Volume 83, Issue 4, pp 317–327 | Cite as

A relation between p-adic L-functions and the Tamagawa number conjecture for Hecke characters

  • Francesc Bars
Original Paper
  • 54 Downloads

Abstract.

We prove that the submodule in K-theory which gives the exact value \(({\text{up to }}\mathbb{Z}_{(p)}^* )\) of the L-function by the Beilinson regulator map at non-critical values for Hecke characters of imaginary quadratic fields K with cl (K)  = 1(p-local Tamagawa number conjecture) satisfies that the length of its coimage under the local Soulé regulator map is the p-adic valuation of certain special values of p-adic L-functions associated to the Hecke characters. This result yields immediately, up to Jannsen’s conjecture, an upper bound for \(\# H_{et}^2 (\mathcal{O}_K [1/S],\;V_p (m))\) in terms of the valuation of these p-adic L-functions, where V p denotes the p-adic realization of a Hecke motive.

Mathematics Subject Classification (2000).

Primary: 11G40 Secondary: 11R23 19F29 

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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra (Barcelona), CatalunyaSpain

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