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Twists of matrix algebras and some subgroups of Brauer groups II

Published online by Cambridge University Press:  17 April 2009

Wenchen Chi
Affiliation:
Department of MathematicsNational Tsing Hua University Hsinchu, Taiwan 30043Republic of China
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Abstract

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We consider some subgroups of Brauer groups arising from twists of matrix algebras by some continuous characters. Explicit descriptions of these subgroups are given in terms of Gauss sums of Dirichlet characters.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Borevich, Z.I. and Shafarevich, I.R., Number theory (Academic Press, New York, 1966).Google Scholar
[2]Chi, W., ‘Twists of central simple algebras and endomorphism algebras of some Abelian varieties’, Math. Ann. 276 (1987), 615632.CrossRefGoogle Scholar
[3]Chi, W., ‘Hasse invariants of some endomorphism algebras of Abelian varieties’, Chinese J. Math. 18 (1990), 8794.Google Scholar
[4]Chi, W., ‘Twists of matrix algebras and some subgroups of Brauer groups’, Bull. Austral.Math. Soc. 45 (1992), 377383.CrossRefGoogle Scholar
[5]Chi, W. and Tan, K.S., ‘Twists of matrix algebras and Brauer groups’, preprint.Google Scholar
[6]Draxl, P.K., Skew fields (Cambridge University Press, Cambridge, 1983).CrossRefGoogle Scholar
[7]Reiner, I., Maximal orders (Academic Press, New York, 1975).Google Scholar
[8]Roquette, P., ‘On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras’, Math. Ann. 150 (1963), 411439.CrossRefGoogle Scholar
[9]Washington, L.C., Introduction to cyclotomic fields (Graduate Texts in Mathematics 83, Springer-Verlag, Berlin, Heidelberg, New York, 1982).CrossRefGoogle Scholar
[10]Yamada, T., The Schur subgroup of the Brauer group, Lecture Notes in Math. 397 (Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar