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E(K/k) and other arithmetical invariants for finite Galois extensions

Published online by Cambridge University Press:  22 January 2016

Shin-Ichi Katayama
Shin-Ichi Katayama*
Affiliation:
Department of Mathematics, College of General Education, Tokushima University, Tokushima, 770, Japan
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Let k be an algebraic number field and K be a finite extension of k. Recently, T. Ono defined positive rational numbers E(K/k) and E′(K/k) for K/k. In [7], he investigated some relations between E(K/k) and other cohomological invariants for K/k. He obtained a formula when K is a normal extension of k. In our paper [3], we obtained a similar formula for E′(K/k) in the case of normal extensions K/k. Both proofs essentially use Ono’s results on the Tamagawa number of algebraic tori, on which the formulae themselves do not depend. Hence, in [8], T. Ono posed a problem to give direct proofs of these formulae.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 114 , June 1989 , pp. 135 - 142
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

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