# Lattices in rank one Lie groups over local fields

@article{Lubotzky1991LatticesIR, title={Lattices in rank one Lie groups over local fields}, author={Alexander Lubotzky}, journal={Geometric \& Functional Analysis GAFA}, year={1991}, volume={1}, pages={405-431} }

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.

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