On the Local Tamagawa Number Conjecture for Tate Motives over Tamely Ramified Fields
نویسنده
چکیده
The local Tamagawa number conjecture, which was first formulated by Fontaine and Perrin-Riou, expresses the compatibility of the (global) Tamagawa number conjecture on motivic L-functions with the functional equation. The local conjecture was proven for Tate motives over finite unramified extensions K/Qp by Bloch and Kato. We use the theory of (φ,Γ)-modules and a reciprocity law due to Cherbonnier and Colmez to provide a new proof in the case of unramified extensions, and to prove the conjecture for Qp(2) over certain tamely ramified extensions.
منابع مشابه
On the Equivariant Tamagawa Number Conjecture for Tate Motives , Part II . Dedicated to John
Let K be any finite abelian extension of Q, k any subfield of K and r any integer. We complete the proof of the equivariant Tamagawa Number Conjecture for the pair (h(Spec(K))(r),Z[Gal(K/k)]). 2000 Mathematics Subject Classification: Primary 11G40; Secondary 11R65 19A31 19B28
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