On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results
نویسندگان
چکیده
منابع مشابه
On the Equivariant Tamagawa Number Conjecture for Tate Motives and Unconditional Annihilation Results
Let L/K be a finite Galois extension of number fields with Galois group G. Let p be a prime and let r ≤ 0 be an integer. By examining the structure of the p-adic group ring Zp[G], we prove many new cases of the p-part of the equivariant Tamagawa number conjecture (ETNC) for the pair (h(Spec(L))(r),Z[G]). The same methods can also be applied to other conjectures concerning the vanishing of certa...
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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 Cherbonn...
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We give a survey of the equivariant Tamagawa number (a.k.a. Bloch-Kato) conjecture with particular emphasis on proven cases. The only new result is a proof of the 2-primary part of this conjecture for Tate-motives over abelian fields. This article is an expanded version of a survey talk given at the conference on Stark’s conjecture, Johns Hopkins University, Baltimore, August 5-9, 2002. We have...
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Let L/K be a nite Galois CM-extension of number elds with Galois group G. In an earlier paper, the author has de ned a module SKu(L/K) over the center of the group ring ZG which coincides with the Sinnott-Kurihara ideal if G is abelian and, in particular, contains many Stickelberger elements. It was shown that a certain conjecture on the integrality of SKu(L/K) implies the minus part of the equ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2015
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6453