Geometric & Functional Analysis GAFA

, Volume 1, Issue 4, pp 405–431 | Cite as

Lattices in rank one Lie groups over local fields

  • Alexander Lubotzky


We prove that if\(G = \underline G (K)\) is theK-rational points of aK-rank one semisimple group\(\underline G \) over a non archimedean local fieldK, thenG has cocompact non-arithmetic lattices and if char(K)>0 also non-uniform ones. We also give a general structure theorem for lattices inG, from which we confirm Serre's conjecture that such arithmetic lattices do not satisfy the congruence subgroup property.


General Structure Local Field Structure Theorem Congruence Subgroup Semisimple Group 
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Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Alexander Lubotzky
    • 1
  1. 1.Institute of MathematicsHebrew UniversityJerusalemIsrael

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