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Burns' Equivariant Tamagawa Invariant T Ωloc( N /Q,1) for some Quaternion Fields
Author(s) -
Snaith Victor
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004800
Subject(s) - equivariant map , quaternion , conjecture , invariant (physics) , mathematics , pure mathematics , omega , combinatorics , algebra over a field , mathematical physics , physics , quantum mechanics , geometry
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 Ω loc ( N /Q,1) for some families of quaternion extensions N /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.