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Cyclotomic Galois module structure and the second Chinburg invariant

Published online by Cambridge University Press:  24 October 2008

Victor P. Snaith
Victor P. Snaith
Affiliation:
The Fields Institute for Research in Mathematical Sciences, 185 Columbia Street West, Waterloo, Ontario, Canada, N2L 5Z5
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Abstract

We study the second Chinburg invariant of a Galois extension of number fields. The Chinburg invariant lies in the class-group of the integral group-ring of the Galois group of the extension. A procedure is given whereby to evaluate the invariant in the case of the real cyclotomic case of regular prime power conductor and their subextensions of p-power degree. The invariant is shown to be zero in the latter cases, which yields new examples giving an affirmative answer to a question of Chinburg ([1], p. 358) which has come to be known as ‘Chinburg's Second Conjecture’ ([3], §4·2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 1 , January 1995 , pp. 57 - 82
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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