Inventiones mathematicae

, Volume 92, Issue 2, pp 255–306 | Cite as

On superrigidity and arithmeticity of lattices in semisimple groups over local fields of arbitrary characteristic

  • T. N. Venkataramana


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Artin, E.: Algebraic number and algebraic functions. New York University, 1951 (Polygraphed Notes)Google Scholar
  2. Berberian, S.: Measure and integration. New York: Macmillan 1963Google Scholar
  3. Borel, A.: Linear algebraic groups. New York: Benjamin 1969Google Scholar
  4. Borel, A., Harder, G.: Existence of discrete cocompact subgroups of reductive groups over local fields. J. Reine Angew. Math.298, 53–64 (1978)Google Scholar
  5. Borel, A., Springer, T.A.: Rationality properties of linear algebraic groups, II. Tohoku J. Math.20, 443–497 (1968)Google Scholar
  6. Borel, A., Tits, J.: Groupes réductifs. Publ. Math., Inst. Hautes Etud. Sci.27, 55–150 (1965)Google Scholar
  7. Borel, A., Tits, J.: Homormorphismes ≪abstraits≫ de groupes algébriques simples. Ann. Math.97, (2) 499–571 (1973)Google Scholar
  8. Cassels, J.W.S.: Local fields. In: Algebraic number theory. New York: Academic Press 1967Google Scholar
  9. Delaroche, C., Kirillov, A.: Sur les relations entre l'espace dual d'un groupe et la structure de ses sousgroupes fermés. Seminaire Bourbaki, No. 343 (1967/68)Google Scholar
  10. Harder, G.: Über die Galoiskohomologie halbeinfacher algebraischer Gruppen III. J. Reine Angew. Math.274/275, 125–138 (1975)Google Scholar
  11. Humphreys, J.: Linear algebraic groups. SLN v. 21, 1975Google Scholar
  12. Kazdan, D.A.: Connection of the dual space of a group with the structure of its closed subgroups. Funct. Anal. Appl.1, 63–65 (1967)Google Scholar
  13. Margulis, G.A.: Cobounded subgroups of algebraic groups over local fields. Funct. Anal. Appl.11, 45–57 (1977)Google Scholar
  14. Margulis, G.A.: Arithmeticity of the irreducible lattices in the semisimple groups of rank greater than 1. Invent. Math.76, 93–120 (1984)Google Scholar
  15. Prasad, G.: Lattices in semisimple groups over local fields. Adv. Math. (supplementary studies)6, 1–86 (1978)Google Scholar
  16. Prasad, G.: Strong approximation for semisimple groups over function fields. Ann. Math.105, 553–572 (1977)Google Scholar
  17. Prasad, G.: Elementary proof of a theorem of Tits. Bull. Soc. Math. France110, 197–202 (1982)Google Scholar
  18. Raghunathan, M.S.: Discrete subgroups of Lie groups. New York: Springer 1972Google Scholar
  19. Serre, J.-P.: Lie algebras and Lie groups. New York: Benjamin 1965Google Scholar
  20. Tamagawa, T.: On discrete Subgroups ofp-adic algebraic groups. In: Arithmetical algebraic geometry, Schilling, U.F.G. (ed.). New York: Harper and Row 1965Google Scholar
  21. Tits, J.: Algebraic and abstract simple groups. Ann. Math.80, 313–329 (1968)Google Scholar
  22. Vinberg, E.B.: Rings of definition of dense subgroups of semisimple linear groups. Groups Math. USSR Izvestija5, 45–55 (1977)Google Scholar
  23. Wang, S.P.: On density properties ofS-groups of locally compact groups. Ann. Math.94, 325–329 (1971)Google Scholar
  24. Weil, A.: Basic Number Theory. Vol. 144, Springer, Berlin, Heidelberg, New York Inc., 1967Google Scholar
  25. Zariski, O., Samuel, P.: Commutative algebra, vol. 1. D. Van Nostrand Company 1967Google Scholar
  26. Zimmer, R.: Ergodic theory and semisimple groups. Boston: Birkhauser 1984Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • T. N. Venkataramana
    • 1
  1. 1.Tata Institute of Fundamental ResearchSchool of MathematicsBombayIndia

Personalised recommendations