Nagoya Mathematical Journal

A cohomological Tamagawa number formula

Annette Huber and Guido Kings

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For smooth linear group 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 defined by Bloch and Kato. We show that in the case of tori, the cohomological and the motivic Tamagawa measures coincide, which proves again the Bloch-Kato conjecture for motives associated to tori.

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Nagoya Math. J., Volume 202 (2011), 45-75.

First available in Project Euclid: 31 May 2011

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Primary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture) 22E41: Continuous cohomology [See also 57R32, 57Txx, 58H10]


Huber, Annette; Kings, Guido. A cohomological Tamagawa number formula. Nagoya Math. J. 202 (2011), 45--75. doi:10.1215/00277630-1260441.

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