Computation of the metaplectic kernel
Publications Mathématiques de l'IHÉS, Tome 84 (1996), pp. 91-187. 
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     title = {Computation of the metaplectic kernel},
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     pages = {91--187},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {84},
     year = {1996},
     mrnumber = {1441007},
     zbl = {0941.22019},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1996__84__91_0/}
}
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Prasad, Gopal; Rapinchuk, Andrei S. Computation of the metaplectic kernel. Publications Mathématiques de l'IHÉS, Tome 84 (1996), pp. 91-187. http://www.numdam.org/item/PMIHES_1996__84__91_0/

[1] E. Artin and J. Tate, Class Field Theory, New York, Benjamin, 1974.

[2] A. Bak, Le problème de sous-groupes congruence et le problème métaplectique pour les groupes classiques de rang > 1, C. R. Acad. Sci. Paris, 292 (1981), 307-310. | MR | Zbl

[3] A. Bak and U. Rehmann, The congruence subgroup and metaplectic problems for SLn ≥ 2 of division algebras, J. Algebra, 78 (1982), 475-547. | MR | Zbl

[4] A. Borel and J. Tits, Groupes réductifs, Publ. Math. I.H.E.S., 27 (1965), 55-150. | Numdam | MR | Zbl

[5] A. Borel and J. Tits, Compléments à l'article “Groupes réductifs”, Publ. Math. I.H.E.S., 41 (1972), 253-276. | Numdam | MR | Zbl

[6] N. Bourbaki, Topologie générale, Ch. 3-4, Paris, Hermann, 1960.

[7] N. Bourbaki, Groupes et algèbres de Lie, Ch. 4-6, Paris, Hermann, 1968.

[8] J. W. S. Cassels and A. Fröhlich (editors), Algebraic number theory (Proc. Instructional Conf., Brighton, 1965), London, Academic Press, and Washington, D. C., Thompson, 1967. | Zbl

[9] P. Deligne, Extensions centrales non résiduellement finies de groupes arithmétiques, C. R. Acad. Sci. Paris, 287 (1978), 203-208. | MR | Zbl

[10] P. Deligne, Extensions centrales de groupes algébriques simplement connexes et cohomologie galoisienne, Publ. Math. I.H.E.S., 84 (1996), 35-89. | Numdam | MR | Zbl

[11] V. Deodhar, On central extensions of rational points of algebraic groups, Amer. J. Math., 100 (1978), 303-386. | MR | Zbl

[12] G. Harder, Über die Galoiskohomologie halbeinfacher algebraischer Gruppen, J. reine und angew. Math., 274-275 (1975), 125-138. | MR | Zbl

[13] S. Helgason, Differential Geometry and Symmetric Spaces, New York, Academic Press, 1962. | MR | Zbl

[14] D. A. Kazhdan and S. J. Patterson, Metaplectic Forms, Publ. Math. I.H.E.S., 59 (1984), 35-142. | Numdam | MR | Zbl

[15] J. Klose, Metaplektische Erweiterungen von Quaternionenschiefkörpern, Math. Z., 193 (1986), 625-649. | MR | Zbl

[16] M. Lazard, Groupes analytiques p-adiques, Publ. Math. I.H.E.S., 26 (1965), 5-219. | Numdam | MR | Zbl

[17] A. Lubotzky, Subgroup growth and congruence subgroups, Invent. Math., 119 (1995), 267-295. | MR | Zbl

[18] G. A. Margulis, Finiteness of quotient groups of discrete groups, Funct. Anal. Appl., 13 (1979), 178-187. | MR | Zbl

[19] G. A. Margulis, On the multiplicative group of a quaternion algebra over a global field, Soviet Math. Dokl., 21 (1980), 780-784. | MR | Zbl

[20] G. W. Mackey, Les ensembles boréliens et les extensions des groupes, J. Math. Pures Appl., 36 (1957), 171-178. | MR | Zbl

[21] H. Matsumoto, Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Sci. École Norm. Sup., 2 (1969), 1-62. | Numdam | MR | Zbl

[22] C. Moore, Group extensions of p-adic and adelic linear groups, Publ. Math. I.H.E.S., 35 (1968), 5-70. | Numdam | MR | Zbl

[23] V. P. Platonov and A. S. Rapinchuk, On the group of rational points of three-dimensional groups, Soviet Math. Dokl., 20 (1979), 693-697. | MR | Zbl

[24] V. P. Platonov and A. S. Rapinchuk, Algebraic Groups and Number Theory, “Pure and Applied Mathematics” series, Vol. 139, New York, Academic Press, 1993. | MR | Zbl

[25] V. P. Platonov and A. S. Rapinchuk, Abstract properties of S-arithmetic groups and the congruence subgroup problem, Russian Acad. Sci. Izv. Math., 40 (1993), 455-476. | MR | Zbl

[26] R. Pierce, Associative Algebras, Heidelberg, Springer Verlag, 1982. | MR | Zbl

[27] G. Prasad, A variant of a theorem of Calvin Moore, C. R. Acad. Sci. Paris, 302 (1986), 405-408. | MR | Zbl

[28] G. Prasad, Semi-simple groups and arithmetic subgroups, Proc. ICM-90 (Kyoto), Vol. II, 821-832. | MR | Zbl

[29] G. Prasad and M. S. Raghunathan, On the congruence subgroup problem : Determination of the metaplectic kernel, Invent. Math., 71 (1983), 21-42. | MR | Zbl

[30] G. Prasad and M. S. Raghunathan, Topological central extensions of semi-simple groups over local fields, Ann. Math., 119 (1984), 143-268. | MR | Zbl

[31] G. Prasad and M. S. Raghunathan, On the Kneser-Tits problem, Comment. Math. Helv., 60 (1985), 107-121. | MR | Zbl

[32] G. Prasad and M. S. Raghunathan, Topological central extensions of SL1(D), Invent. Math., 92 (1988), 645-689. | MR | Zbl

[33] M. S. Raghunathan, Torsion in cocompact lattices in coverings of Spin(2, n), Math. Ann., 266 (1984), 403-419. | MR | Zbl

[34] M. S. Raghunathan, On the group of norm 1 elements in a division algebra, Math. Ann., 279 (1988), 457-484. | MR | Zbl

[35] M. S. Raghunathan, The congruence subgroup problem, Proc. Hyderabad Conf. on Algebraic Groups (ed. by S. Ramanan with the cooperation of C. Musili and N. M. Kumar), Manoj Prakashan, 1991, 465-494. | MR | Zbl

[36] A. S. Rapinchuk, Multiplicative arithmetic of division algebras over number fields and the metaplectic problem, Math. USSR Izvestiya, 31 (1988), 349-379. | MR | Zbl

[37] A. S. Rapinchuk, Combinatorial theory of arithmetic groups, Preprint of the Institute of Mathematics, Acad. Sci. of Belarus (Minsk), No. 20 (420), 1990.

[38] A. S. Rapinchuk, Congruence subgroup problem for algebraic groups : old and new, Astérisque, 209 (1992), 73-84. | MR | Zbl

[39] C. Riehm, The norm 1 group of p-adic division algebra, Amer. J. Math., 92 (1970), 499-523. | MR | Zbl

[40] J.-P. Serre, Cohomologie galoisienne, Lect. Notes Math., No. 5, Heidelberg, Springer Verlag, 1994. | MR | Zbl

[41] J.-P. Serre, Local Fields, Heidelberg, Springer Verlag, 1995.

[42] J.-P. Serre, Lie Algebras and Lie Groups, Lect. Notes Math., No. 1500, Heidelberg, Springer Verlag, 1992. | MR | Zbl

[43] W. Scharlau, Quadratic and hermitian forms, Heidelberg, Springer Verlag, 1985. | MR | Zbl

[44] B. Sury, Congruence subgroup problem for anisotropic groups over semi-local rings, Proc. Indian Acad. Sci., 101 (1991), 87-110. | MR | Zbl

[45] R. G. Thompson, Commutators in the special and general linear groups, Trans. A.M.S., 101 (1961), 16-33. | MR | Zbl

[46] J. Tits, Classification of algebraic semisimple groups, Algebraic Groups and Discontinuous Subgroups, Proc. Symp. Pure Math., Vol. 9, Amer. Math. Soc., Providence, R. I., 1966, 33-62. | MR | Zbl

[47] D. Toledo, Projective varieties with non-residually finite fundamental group, Publ. Math. I.H.E.S., 77 (1993), 103-119. | Numdam | MR | Zbl

[48] G. Tomanov, On Grunwald-Wang's theorem, J. reine und angew. Math., 389 (1988), 209-220. | MR | Zbl

[49] B. Weisfeiler, Semi-simple algebraic groups splitting over a quadratic extension, Math. USSR Izvestiya, 5 (1971), 57-73. | Zbl

[50] D. Wigner, Algebraic cohomology of topological groups, Trans. A.M.S., 178 (1973), 83-93. | MR | Zbl