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Discrete subgroups of algebraic groups over local fields of positive characteristics. (English) Zbl 0689.22004
It is shown in this paper that if G is the group of k-points of a semisimple algebraic group G over a local field k of positive characteristic such that all its k-simple factors are of k-rank 1 and $$\Gamma$$ $$\subset G$$ is an irreducible lattice then $$\Gamma$$ admits a fundamental domain which is a union of translates of Siegel domains. As a consequence the author deduces that if G has more than one simple factor, then $$\Gamma$$ is finitely generated and, by a theorem due to Venkataramana, it is arithmetic. The new result here is the case of a non-cocompact $$\Gamma$$. The results are stated in an apparently more general context, namely for a discrete subgroup $$\Gamma$$ of G which is what is called an L-subgroup. It turns out that any L-group in G is indeed a lattice.
Reviewer: H.Abels

##### MSC:
 22E40 Discrete subgroups of Lie groups 20G25 Linear algebraic groups over local fields and their integers
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##### References:
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