Lattices in rank one Lie groups over local fields

  title={Lattices in rank one Lie groups over local fields},
  author={A. Lubotzky},
  journal={Geometric \& Functional Analysis GAFA},
  • A. Lubotzky
  • Published 1991
  • Mathematics
  • Geometric & Functional Analysis GAFA
AbstractWe 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.