Tamagawa Kidunano-Mori

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Notes on Tamagawa Number

Remark 2. It looks like from the definition τ(G) depends on the number field K, so it should be τK(G). If L is a finite extension of K, we have τL(G) = τK(RL/K(G)). Weil showed that in fact the Tamagawa number is independent of Weil restriction, i.e., τL(G) = τK(RL/K(G)) = τK(G). This is proved with details in the paper by Oesterlé ”Nombres de Tamagawa et groupes unipotentes en caractéristique ...

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Let K be a number field, and let A/K be an abelian variety. Let c denote the product of the Tamagawa numbers of A/K, and let A(K)tors denote the finite torsion subgroup of A(K). The quotient c/|A(K)tors| is a factor appearing in the leading term of the L-function of A/K in the conjecture of Birch and Swinnerton-Dyer. We investigate in this article possible cancellations in this ratio. Precise r...

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A cohomological Tamagawa number formula

For smooth linear groups schemes over Z we give a cohomological interpretation of the local Tamagawa measures as cohomological periods. This is in the spirit of the Tamagawa measures for motives de ned by Bloch and Kato. We show that in the case of tori the cohomological and the motivic Tamagawa measures coincide, which reproves the Bloch-Kato conjecture for motives associated to tor

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ژورنال

عنوان ژورنال: Journal of the Japanese Institute of Landscape Architecture

سال: 1997

ISSN: 1348-4559,1340-8984

DOI: 10.5632/jila.61.304