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Unit theorems on algebraic tori

Published online by Cambridge University Press:  22 January 2016

Hyun Kwang Kim
Hyun Kwang Kim*
Affiliation:
Department of Mathematics, Pohang Institute of Science and Technology, P.O. Box 125 POHANG 790, KOREA
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Let k be a p-adic field (a finite extension of Qp) or an algebraic number field (a finite extension of Q). Let T be an algebraic torus defined over k. We denote by the character module of T (i.e. = Hom (T, Gm), where Gm is the multiplicative group.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 112 , December 1988 , pp. 117 - 124
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

[1] Artin, E., Über Einheiten relativ galoisscher Zählkörper, Crelle Journal, 167 (1932), 153–156.Google Scholar
[2] Curtis, C. W. and Reiner, I., Methods of representation theory with application to finite groups and orders, 1, John Wiley & Sons Inc., 1981.Google Scholar
[3] Herbrand, M. J., Nouvelle démonstration et généralisation d’un théorème de Minkowski, Comptes rendus, 191 (1930), 1282–1285.Google Scholar
[4] Herbrand, M. J., Sur les unités d’un corps algébrique, Comptes rendus, 192 (1931), 24–27.Google Scholar
[5] Long, R. L., Algebraic number theory, Marcel Dekker Inc., 1977, pp. 57–65.Google Scholar
[6] Ono, T., On some arithmetic properties of linear algebraic groups, Ann. of Math., 70, no. 2 (1959), 266–290.CrossRefGoogle Scholar
[7] Ono, T., Arithmetic of algebraic tori, Ann. of Math., v. 74, no. 1 (1961), 101–119.CrossRefGoogle Scholar
[8] Ono, T., Arithmetic of algebraic groups and its applications, Lecture Notes, Rikkyo 1986.Google Scholar
[9] Weil, A., Adeles and algebraic groups, Birkhäuser, 1982.CrossRefGoogle Scholar