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A cohomological Tamagawa number formula

Published online by Cambridge University Press:  11 January 2016

Annette Huber  and
Guido Kings
Annette Huber
Affiliation:
Mathematisches Institut, Universität Freiburg, 9102 Freiburg, Germanyannette.huber@math.uni-freiburg.de
Guido Kings
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germanyguido.kings@mathematik.uni-regensburg.de
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Abstract

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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.

Keywords

11G4011R4214G1022E41
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 202 , June 2011 , pp. 45 - 75
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

References

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