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A Note on Galois Cohomology Groups of Algebraic Tori

Published online by Cambridge University Press:  22 January 2016

Kazuo Amano
Kazuo Amano*
Affiliation:
Mathematical Institute, Nagoya University
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Let k be a complete field of characteristic 0 whose topology is defined by a discrete valuation and let T be an algebraic torus of dimension d defined over k. As is well known, T has a splitting field K which is a finite Galois extension of k with Galois group . For a ring R, denote by TR the subgroup of R-rational points of T. Then TK and T0K, DK being a valuation ring of K, become -modules in the usual manner.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 34 , March 1969 , pp. 121 - 127
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

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