, Volume 76, Issue 1-2, pp 113-128

Finiteness properties of certain arithmetic groups in the function field case

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Abstract

It is proved that the finiteness length of Γ=SL n (ℱ q [t]) isn−2 ifn≥2 andq≥2 n−2. The proof consists in studying the homotopy type of a certain Γ-invariant filtration of an appropriate Bruhat-Tits building on which Γ acts.