@article{PMIHES_1989__69__119_0, author = {Borel, Armand and Prasad, Gopal}, title = {Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {119--171}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {69}, year = {1989}, mrnumber = {1019963}, zbl = {0707.11032}, language = {en}, url = {http://www.numdam.org/item/PMIHES_1989__69__119_0/} }
TY - JOUR AU - Borel, Armand AU - Prasad, Gopal TI - Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups JO - Publications Mathématiques de l'IHÉS PY - 1989 SP - 119 EP - 171 VL - 69 PB - Institut des Hautes Études Scientifiques UR - http://www.numdam.org/item/PMIHES_1989__69__119_0/ LA - en ID - PMIHES_1989__69__119_0 ER -
%0 Journal Article %A Borel, Armand %A Prasad, Gopal %T Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups %J Publications Mathématiques de l'IHÉS %D 1989 %P 119-171 %V 69 %I Institut des Hautes Études Scientifiques %U http://www.numdam.org/item/PMIHES_1989__69__119_0/ %G en %F PMIHES_1989__69__119_0
Borel, Armand; Prasad, Gopal. Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups. Publications Mathématiques de l'IHÉS, Tome 69 (1989), pp. 119-171. http://www.numdam.org/item/PMIHES_1989__69__119_0/
[1] Counting points on curves over finite fields (d'après S. A. STEPANOV), Séminaire Bourbaki, Springer L.N.M., 383 (1974). | Numdam | MR | Zbl
,[2] Some finiteness properties of adele groups over number fields, Publ. Math. I.H.E.S., 16 (1963), 5-30. | Numdam | MR | Zbl
,[3] On the set of discrete subgroups of bounded covolume in a semi-simple group, Proc. Indian Acad. Sci. (Math. Sci.), 97 (1987), 45-52. | MR | Zbl
,[4] Sous-groupes discrets de groupes p-adiques à covolume borné, C. R. Acad. Sc. Paris, 305 (1987), 357-362. | MR | Zbl
et ,[5] Théorèmes de finitude en cohomologie galoisienne, Comment. Math. Helv., 39 (1964), 111-164. | MR | Zbl
et ,[6] Cohomologie d'immeubles et de groupes S-arithmétiques, Topology, 15 (1976), 211-232. | MR | Zbl
et ,[7] Homomorphismes "abstraits" de groupes algébriques simples, Ann. Math., 97 (1973), 499-571. | MR | Zbl
et ,[8] Groupes réductifs sur un corps local, I, Pub. Math. I.H.E.S., 41 (1971), 5-251 ; II, ibid., 60 (1984), 5-184 ; III, J. Fac. Sci. Univ. Tokyo (Sec. IA), 34 (1987), 671-698. | Zbl
et ,[9] Introduction to the theory of algebraic functions of one variable, Math. Surveys, Number 6, A.M.S. (1951). | MR | Zbl
,[10] Volumes of hyperbolic manifolds, J. Diff. Geom., 18 (1983), 783-789. | MR | Zbl
,[11] Lectures on the theory of algebraic functions of one variable, Springer L.N.M., 314 (1973). | MR | Zbl
,[12] Field arithmetic, Berlin, Springer-Verlag (1986). | MR | Zbl
and ,[13] Cohomologie non abélienne, Grund. Math. Wiss., Springer-Verlag, 1971. | Zbl
,[14] Minkowskische Reduktionstheorie über Funktionenkörpern, Invent. Math., 7 (1969), 33-54. | MR | Zbl
,[15] Über die Galoiskohomologie halbeinfacher algebraischer Gruppen III, J. Reine Angew. Math. 274/275 (1975), 125-138. | MR | Zbl
,[16] On some Bruhat decompositions and the structure of the Hecke rings of the p-adic Chevalley groups, Publ. Math. I.H.E.S., 25 (1965), 5-48. | Numdam | MR | Zbl
and ,[17] On discrete chamber-transitive automorphism groups of affine buildings, Bull. A.M.S., 16 (1987), 129-133. | MR | Zbl
, and ,[18] Tamagawa numbers, Ann. Math., 127 (1988), 629-646. | MR | Zbl
,[19] Galoiskohomologie halbeinfacher algebraischer Gruppen über p-adischen Körpern, I, II, Math. Z., 88 (1965), 250-272. | Zbl
,[20] Algebraic number theory, Addison-Wesley, Reading, Mass. (1968).
,[21] Algebra, Addison-Wesley, Reading, Mass. (1965). | MR | Zbl
,[22] Cobounded subgroups of algebraic groups over local fields, Funct. Anal. Appl., 11 (1977), 45-57. | MR | Zbl
,[23] Arithmeticity of the irreducible lattices in the semi-simple groups of rank greater than I, Invent. Math., 76 (1984), 93-120. | MR | Zbl
,[24] On the proportionality of covolumes of discrete subgroups, Math. Ann., 275 (1986), 197-205. | MR | Zbl
and ,[25] Étale Cohomology, Princeton U. Press (1980). | MR | Zbl
,[26] Some analytic estimates of class numbers and discriminants, Invent. Math., 29 (1975), 275-286. | MR | Zbl
,[27] Lower bounds for discriminants of number fields, Acta Arith., 29 (1976), 275-297. | MR | Zbl
,[28] Nombres de Tamagawa et groupes unipotents en caractéristique p, Invent. Math., 78 (1984), 13-88. | MR | Zbl
,[29] Minorations de discriminants (d'après A. M. ODLYZKO), Sém. Bourbaki, Springer L.N.M., 567 (1977). | Numdam | MR | Zbl
,[30] Strong approximation, Ann. Math., 105 (1977), 553-572. | MR | Zbl
,[31] Volumes of S-arithmetic quotients of semi-simple groups, Publ. Math. I.H.E.S., 69 (1989), 91-117. | Numdam | MR | Zbl
,[32] Die maximalen arithmetisch definierten Untergruppen zerfallender einfacher Gruppen, Math. Ann., 244 (1979), 219-231. | MR | Zbl
,[33] Cohomologie des groupes discrets, in Ann. of Math. Studies, 70, Princeton University Press (1971). | Zbl
,[34] Profinite groups, arithmetic and geometry, Ann. of Math. Studies, 67, Princeton University Press, 1972. | MR | Zbl
,[35] Über die Classenzahl quadratischer Zahlkörper, Acta. Arith., 1 (1936), 83-86. | JFM | Zbl
,[36] Die Theorie der Gruppen von endlicher Ordnung, Grund. Math. Wiss., 5, Springer-Verlag.
,[37] Conjugacy classes, in Springer L.N.M., 131 (1970), 167-294. | MR | Zbl
and ,[38] Regular elements of semi-simple algebraic groups, Publ. Math. I.H.E.S., 25 (1965), 49-80. | Numdam | MR | Zbl
,[39] Endomorphisms of linear algebraic groups, Mem. A.M.S., 80 (1968). | MR | Zbl
,[40] Classification of algebraic semi-simple groups, Proc. A.M.S. Symp. Pure Math., 9 (1966), 33-62. | MR | Zbl
,[41] Reductive groups over local fields, Proc. A.M.S. Symp. Pure Math., 33, Part 1 (1979). | MR | Zbl
,[42] Buildings and group amalgamations, in Groups St. Andrews 1985, Cambridge University Press, 1987, 110-127. | MR | Zbl
,[43] On superrigidity and arithmeticity of lattices in semi-simple groups, Invent. Math., 92 (1988), 255-306. | MR | Zbl
,[44] Topics on totally discontinuous groups, in Symmetric spaces (ed. by W. M. BOOTHBY and G. WEISS), New York, Marcel Dekker (1972), 459-487. | MR | Zbl
,[45] Basic number theory, Berlin, Springer-Verlag. | Zbl
,[46] Adeles and algebraic groups, Progress in Math., 23 (1982), Birkhäuser, Boston. | MR | Zbl
,[47] Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung, Invent. Math., 62 (1981), 367-380. | MR | Zbl
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