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On the Galois Cohomology Group of the Ring of Integers in a Global Field and its Adele Ring

Published online by Cambridge University Press:  22 January 2016

Yoshiomi Furuta  and
Yasuaki Sawada
Yoshiomi Furuta
Affiliation:
Kanazawa University, Kanazawa Institute of Technology
Yasuaki Sawada
Affiliation:
Kanazawa University, Kanazawa Institute of Technology
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By a global field we mean a field which is either an algebraic number field, or an algebraic function field in one variable over a finite constant field. The purpose of the present note is to show that the Galois cohomology group of the ring of integers of a global field is isomorphic to that of the ring of integers of its adele ring and is reduced to asking for that of the ring of local integers.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 247 - 252
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Weiss, E.: Algebraic Number Theory, McGraw-Hill (1963).Google Scholar
[2] Yokoi, H.: On the ring of integers in an algebraic number field as a representation module of Galois group, Nagoya Math. J., 16 (1960).CrossRefGoogle Scholar
[3] Yokoi, H.: On the Galois cohomology group of the ring of integers in an algebraic number field, Acta Arithmetica VIII (1963).Google Scholar
[4] Yokoi, H.: A note on the Galois cohomology group of the ring of integers in an algebraic number field, Proc. Japan Acad., 40 (1964).Google Scholar