Finiteness theorems for discrete subgroups of bounded covolume in semi- simple groups
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Publication:919387
DOI10.1007/BF02698843zbMath0707.11032MaRDI QIDQ919387
Publication date: 1989
Published in: Publications Mathématiques (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=PMIHES_1989__69__119_0
Discrete subgroups of Lie groups (22E40) Structure of modular groups and generalizations; arithmetic groups (11F06) Linear algebraic groups over local fields and their integers (20G25)
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Cites Work
- Unnamed Item
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- Homomorphismes abstraits de groupes algébriques simples
- Nombres de Tamagawa et groupes unipotents en caractéristique p
- Arithmeticity of the irreducible lattices in the semi-simple groups of rank greater than 1
- Volumes of S-arithmetic quotients of semi-simple groups. With an appendix by Moshe Jarden and Gopal Prasad
- Volumes of hyperbolic manifolds
- On superrigidity and arithmeticity of lattices in semisimple groups over local fields of arbitrary characteristic
- On the set of discrete subgroups of bounded covolume in a semisimple group
- Tamagawa numbers
- Die maximalen arithmetisch definierten Untergruppen zerfallender einfacher Gruppen
- Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung
- Adèles and algebraic groups. (Appendix 1: The case of the group \(G_2\), by M. Demazure. Appendix 2: A short survey of subsequent research on Tamagawa numbers, by T. Ono)
- Cohomologie d'immeubles et de groupes S-arithmétiques
- Strong approximation for semi-simple groups over function fields
- Cobounded subgroups of algebraic groups over local fields
- Some finiteness properties of adele groups over number fields
- Théoremes de finitude en cohomologie galoisienne
- On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups
- Minkowskische Reduktionstheorie über Funktionenkörpern
- Lectures on the theory of algebraic functions of one variable
- On discrete chamber-transitive automorphism groups of affine buildings
- Über die Galoiskohomologie halbeinfacher algebraischer Gruppen. III.
- Minorations de discriminants [d’après A. M. Odlyzko]
- Über die Classenzahl quadratischer Zahlkörper
- Lower bounds for discriminants of number fields
- Endomorphisms of linear algebraic groups
- Profinite Groups, Arithmetic, and Geometry. (AM-67)
- Some analytic estimates of class numbers and discriminants
