Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups
Publications Mathématiques de l'IHÉS, Tome 69 (1989), pp. 119-171. 
@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://archive.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://archive.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://archive.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://archive.numdam.org/item/PMIHES_1989__69__119_0/

[1] E. Bombieri, Counting points on curves over finite fields (d'après S. A. STEPANOV), Séminaire Bourbaki, Springer L.N.M., 383 (1974). | Numdam | MR | Zbl

[2] A. Borel, Some finiteness properties of adele groups over number fields, Publ. Math. I.H.E.S., 16 (1963), 5-30. | Numdam | MR | Zbl

[3] A. Borel, 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] A. Borel et G. Prasad, Sous-groupes discrets de groupes p-adiques à covolume borné, C. R. Acad. Sc. Paris, 305 (1987), 357-362. | MR | Zbl

[5] A. Borel et J.-P. Serre, Théorèmes de finitude en cohomologie galoisienne, Comment. Math. Helv., 39 (1964), 111-164. | MR | Zbl

[6] A. Borel et J.-P. Serre, Cohomologie d'immeubles et de groupes S-arithmétiques, Topology, 15 (1976), 211-232. | MR | Zbl

[7] A. Borel et J. Tits, Homomorphismes "abstraits" de groupes algébriques simples, Ann. Math., 97 (1973), 499-571. | MR | Zbl

[8] F. Bruhat et J. Tits, 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

[9] C. Chevalley, Introduction to the theory of algebraic functions of one variable, Math. Surveys, Number 6, A.M.S. (1951). | MR | Zbl

[10] T. Chinburg, Volumes of hyperbolic manifolds, J. Diff. Geom., 18 (1983), 783-789. | MR | Zbl

[11] M. Deuring, Lectures on the theory of algebraic functions of one variable, Springer L.N.M., 314 (1973). | MR | Zbl

[12] M. Fried and M. Jarden, Field arithmetic, Berlin, Springer-Verlag (1986). | MR | Zbl

[13] F. Giraud, Cohomologie non abélienne, Grund. Math. Wiss., Springer-Verlag, 1971. | Zbl

[14] G. Harder, Minkowskische Reduktionstheorie über Funktionenkörpern, Invent. Math., 7 (1969), 33-54. | MR | Zbl

[15] G. Harder, Über die Galoiskohomologie halbeinfacher algebraischer Gruppen III, J. Reine Angew. Math. 274/275 (1975), 125-138. | MR | Zbl

[16] N. Iwahori and H. Matsumoto, 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

[17] W. M. Kantor, R. A. Liebler and J. Tits, On discrete chamber-transitive automorphism groups of affine buildings, Bull. A.M.S., 16 (1987), 129-133. | MR | Zbl

[18] R. E. Kottwitz, Tamagawa numbers, Ann. Math., 127 (1988), 629-646. | MR | Zbl

[19] M. Kneser, Galoiskohomologie halbeinfacher algebraischer Gruppen über p-adischen Körpern, I, II, Math. Z., 88 (1965), 250-272. | Zbl

[20] S. Lang, Algebraic number theory, Addison-Wesley, Reading, Mass. (1968).

[21] S. Lang, Algebra, Addison-Wesley, Reading, Mass. (1965). | MR | Zbl

[22] G. A. Margulis, Cobounded subgroups of algebraic groups over local fields, Funct. Anal. Appl., 11 (1977), 45-57. | MR | Zbl

[23] G. A. Margulis, Arithmeticity of the irreducible lattices in the semi-simple groups of rank greater than I, Invent. Math., 76 (1984), 93-120. | MR | Zbl

[24] G. A. Margulis and J. Rohlfs, On the proportionality of covolumes of discrete subgroups, Math. Ann., 275 (1986), 197-205. | MR | Zbl

[25] J. S. Milne, Étale Cohomology, Princeton U. Press (1980). | MR | Zbl

[26] A. M. Odlyzko, Some analytic estimates of class numbers and discriminants, Invent. Math., 29 (1975), 275-286. | MR | Zbl

[27] A. M. Odlyzko, Lower bounds for discriminants of number fields, Acta Arith., 29 (1976), 275-297. | MR | Zbl

[28] J. Oesterlé, Nombres de Tamagawa et groupes unipotents en caractéristique p, Invent. Math., 78 (1984), 13-88. | MR | Zbl

[29] G. Poitou, Minorations de discriminants (d'après A. M. ODLYZKO), Sém. Bourbaki, Springer L.N.M., 567 (1977). | Numdam | MR | Zbl

[30] G. Prasad, Strong approximation, Ann. Math., 105 (1977), 553-572. | MR | Zbl

[31] G. Prasad, Volumes of S-arithmetic quotients of semi-simple groups, Publ. Math. I.H.E.S., 69 (1989), 91-117. | Numdam | MR | Zbl

[32] J. Rohlfs, Die maximalen arithmetisch definierten Untergruppen zerfallender einfacher Gruppen, Math. Ann., 244 (1979), 219-231. | MR | Zbl

[33] J.-P. Serre, Cohomologie des groupes discrets, in Ann. of Math. Studies, 70, Princeton University Press (1971). | Zbl

[34] S. S. Shatz, Profinite groups, arithmetic and geometry, Ann. of Math. Studies, 67, Princeton University Press, 1972. | MR | Zbl

[35] C. L. Siegel, Über die Classenzahl quadratischer Zahlkörper, Acta. Arith., 1 (1936), 83-86. | JFM | Zbl

[36] A. Speiser, Die Theorie der Gruppen von endlicher Ordnung, Grund. Math. Wiss., 5, Springer-Verlag.

[37] T. A. Springer and R. Steinberg, Conjugacy classes, in Springer L.N.M., 131 (1970), 167-294. | MR | Zbl

[38] R. Steinberg, Regular elements of semi-simple algebraic groups, Publ. Math. I.H.E.S., 25 (1965), 49-80. | Numdam | MR | Zbl

[39] R. Steinberg, Endomorphisms of linear algebraic groups, Mem. A.M.S., 80 (1968). | MR | Zbl

[40] J. Tits, Classification of algebraic semi-simple groups, Proc. A.M.S. Symp. Pure Math., 9 (1966), 33-62. | MR | Zbl

[41] J. Tits, Reductive groups over local fields, Proc. A.M.S. Symp. Pure Math., 33, Part 1 (1979). | MR | Zbl

[42] J. Tits, Buildings and group amalgamations, in Groups St. Andrews 1985, Cambridge University Press, 1987, 110-127. | MR | Zbl

[43] T. N. Venkataramana, On superrigidity and arithmeticity of lattices in semi-simple groups, Invent. Math., 92 (1988), 255-306. | MR | Zbl

[44] H. C. Wang, 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] A. Weil, Basic number theory, Berlin, Springer-Verlag. | Zbl

[46] A. Weil, Adeles and algebraic groups, Progress in Math., 23 (1982), Birkhäuser, Boston. | MR | Zbl

[47] R. Zimmert, Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung, Invent. Math., 62 (1981), 367-380. | MR | Zbl