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BURNS' EQUIVARIANT TAMAGAWA INVARIANT $T\Omega{^{\rm loc}}(N/{\bf Q},1)$ FOR SOME QUATERNION FIELDS

Published online by Cambridge University Press:  17 November 2003

VICTOR SNAITH
VICTOR SNAITH
Affiliation:
School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ
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Abstract

Inspired by the work of Bloch and Kato in [2], David Burns constructed several ‘equivariant Tamagawa invariants’ associated to motives of number fields. These invariants lie in relative $K$-groups of group-rings of Galois groups, and in [3] Burns gave several conjectures (see Conjecture 3.1) about their values. In this paper I shall verify Burns' conjecture concerning the invariant $T\Omega^{\rm loc}( N/{\bf Q},1)$ for some families of quaternion extensions $N/{\bf Q}$. Using the results of [9] I intend in a subsequent paper to verify Burns' conjecture for those families of quaternion fields which are not covered here.

Keywords

11R33 (primary)11R2311R65 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 599 - 614
Copyright
The London Mathematical Society 2003

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