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On a classification of the function fields of algebraic tori

Published online by Cambridge University Press:  22 January 2016

Shizuo Endo and
Takehiko Miyata
Shizuo Endo
Affiliation:
Tokyo Metropolitan University, Osaka City University
Takehiko Miyata
Affiliation:
Tokyo Metropolitan University, Osaka City University
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Let II be a finite group and denote by MII the class of all (finitely generated Z-free) II-modules. In the previous paper [3] we defined an equivalence relation in MII and constructed the abelian semigroup T(II) by giving an addition to the set of all equivalence classes in MII . The investigation of the semigroup T(II) seems interesting and important, because this gives a classification of the function fields of algebraic tori defined over a field k which split over a Galois extension of k with group II.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975, pp. 85 - 104
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Chevalley, C., On algebraic group varieties, J. Math. Soc. Japan, 6 (1954), 303–324.Google Scholar
[2] Endo, S. and Miyata, T., Invariants of finite abelian groups, J. Math. Soc. Japan, 25 (1973), 7–26.Google Scholar
[3] Endo, S. and Miyata, T., Quasi-permutation modules over finite groups, J. Math. Soc. Japan, 25 (1973), 397–421.Google Scholar
[4] Endo, S. and Miyata, T., Quasi-permutation modules over finite groups, II, J. Math. Soc. Japan, 26 (1974), 698–713.CrossRefGoogle Scholar
[5] Jacobinski, H., Genera and decompositions of lattices over orders, Acta Math., 121 (1968), 1–29.Google Scholar
[6] Lenstra, H. W. Jr., Rational functions invariant under a finite abelian group, Preprint, Univ. Amsterdam, 1972.Google Scholar
[7] Ono, T., Arithmetic of algebraic tori, Ann. of Math., 74 (1961), 101–139.Google Scholar
[8] Ono, T., On the Tamagawa number of algebraic tori, Ann. of Math., 78 (1963), 47–73.CrossRefGoogle Scholar
[9] Rosen, M., Representations of twisted group rings, Thesis at Princeton Univ., 1963.Google Scholar
[10] Swan, R. G., Projective modules over group rings and maximal orders, Ann. of Math., 76 (1962), 55–61.Google Scholar
[11] Swan, R. G., The Grothendieck ring of a finite group, Topology, 2 (1963), 85–110.Google Scholar
[12] Swan, R. G., Invariant rational functions and a problem of Steenrod, Invent. Math., 7 (1969), 148–158.Google Scholar
[13] Voskresenskiĭ, V. E., Birational properties of linear algebraic groups, Izv. Akad. Nauk. SSSR, 34 (1970), 3–19.Google Scholar