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A variant of Moore's uniqueness of reciprocity laws

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  26 February 2010

B. Sury
B. Sury
Affiliation:
School of Mathematics, T.I.F.R., HomiBhabha Road, BOMBAY 400005, INDIA.
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Abstract

In the case of F-isotropic groups for a global field F, Moore [Mo] computed the metaplectic kernel using crucially his theorem of uniqueness of reciprocity laws. For F-anisotropic G, a variant of Moore's theorem is, therefore, needed to compute the metaplectic kernel. Such a variant was announced by G. Prasad [GP1] (in 1986) and here we give the details.

MSC classification

Secondary: 11R99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 246 - 255
Copyright
Copyright © University College London 1993

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References

B-M-S.Bass, H., Milnor, J. and Serre, J.-P.. Solution of the congruence subgroup problem for SL(n) and Sp(2n). Publ. Math. IHES, (1967), 421–99.Google Scholar
C-W.Chase, S. U. and Waterhouse, W.: Moore's theorem on uniqueness of reciprocity laws. Inv. Math., 16 (1972), 267–270.CrossRefGoogle Scholar
Mo.Moore, C. C.. Group extension of p-ndic and adelic linear groups. Publ. Math. IHES, 35 (1968), 157–222.Google Scholar
GP1.Prasad, G.. Une variante du theoreme de Calvin Moore. C.R. Acad. Sci. Paris, 302 (1986), 405–408.Google Scholar
GP2.Prasad, G.. On the wild norm residue symbol in an abelian extension. Math. Ann. 274 (1986), 419–422.CrossRefGoogle Scholar
P-R.Prasad, G. and Raghunathan, M. S.. On the congruence subgroup problem: determination of the ‘metaplectic kernel’. Inv. Math., 71 (1983), 21–42.CrossRefGoogle Scholar
R.Rapinchuk, A. S.. Multiplicative arithmetic of division algebras over number fields and the metaplectic problem. Math. USSR Izv., 31 (1988), 349–379.CrossRefGoogle Scholar