Lattices in rank one Lie groups over local fields

Alexander Lubotzky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

62 Scopus citations

Abstract

We prove that if {Mathematical expression} is the K-rational points of a K-rank one semisimple group {Mathematical expression} over a non archimedean local field K, then G has cocompact non-arithmetic lattices and if char(K)>0 also non-uniform ones. We also give a general structure theorem for lattices in G, from which we confirm Serre's conjecture that such arithmetic lattices do not satisfy the congruence subgroup property.

Original languageEnglish
Pages (from-to)405-431
Number of pages27
JournalGeometric and Functional Analysis
Volume1
Issue number4
DOIs
StatePublished - Dec 1991

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