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Cohomological characterization of the Hilbert symbol over Q*p

Part of: Special aspects of infinite or finite groups $K$-theory in number theory

Published online by Cambridge University Press:  09 April 2009

Fernando Pablos Romo
Fernando Pablos Romo
Affiliation:
Department de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain, e-mail: fpablos@usal.es
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Abstract

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The aim of this work is to offer a new characterization of the Hilbert symbol Q*p from the commutator of a certain central extension of groups. We obtain a characterization for Q*p (p≠2) and a different one for Q*2.

MSC classification

Secondary: 19F15: Symbols and arithmetic 20F12: Commutator calculus
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 3 , December 2005 , pp. 361 - 368
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Arbarello, E., de Concini, C. and Kac, V. G., ‘The infinite wedge representation and the reciprocity law for algebraic curves’, in: Theta functions - Bowdoin 1987 (Brunswick, ME, 1987), Proc. Sympos. Pure Math. 49, Part I (Amer. Math. pubn., Providence, RI, 1989) pp. 171–190.Google Scholar
[2]Milnor, J., Introduction to algebraic K-theory, Ann. of Math. Stud. 72 (Princeton University Press, Princeton, 1971).Google Scholar
[3]Romo, F. Pablos, ‘On the tame symbol of an algebraic curve’, Comm. Algebra 30 (2002), 4349–4368.Google Scholar
[4]Romo, F. Pablos, ‘Algebraic construction of the tame symbol and the Parshin symbol on a surface’, J. Algebra 274 (2004), 335–346.Google Scholar
[5]Serre, J. P., Groupes algébriques et corps de classes (Hermann, Paris, 1959).Google Scholar
[6]Serre, J. P., A course in arithmetic (Springer, New York, 1973).CrossRefGoogle Scholar
[7]Tate, J., ‘Residues of differentials on curves’, Ann. Sci. École Norm. Sup. 4 (1968), 149–159.CrossRefGoogle Scholar