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A local-global principle for finiteness properties ofS-arithmetic groups over number fields

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Abstract

In the preceding paper [AT] compactness propertiesC n andCP n for locally compact groups were introduced. They generalize the finiteness propertiesF n andFP n for discrete groups. In this paper a local-global principle forS-arithmetic groups over number fields is proved. TheS-arithmetic group г is of typeF n , resp.FP n , if and only if for allp inS thep-adic completionG p of the corresponding algebraic groupG is of typeC n resp.CP n . As a corollary we obtain an easy proof of a theorem of Borel and Serre: AnS-arithmetic subgroup of a semisimple group has all the finiteness propertiesF n .

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  1. Israel Development Center, Intel Israel (74) ltd., P.O. Box 1659, 31015, Haifa, Israel

    A. Tiemeyer

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  1. A. Tiemeyer
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Tiemeyer, A. A local-global principle for finiteness properties ofS-arithmetic groups over number fields. Transformation Groups 2, 215–223 (1997). https://doi.org/10.1007/BF01235942

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  • DOI: https://doi.org/10.1007/BF01235942

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