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Special Arithmetic Subgroups of Chevalley Groups

Introduction. Let k be an algebraic number field, and G an almost simple, simply connected linear algebraic group defined over k. Assume G is embedded over k in GL(V) where V is a finite dimensional vector space defined over k. Let L C V(k) be a lattice, and for each prime p of the ring of integers let Lp be its closure in V(kp). We denote by r, r, the stabilizers in G(k), G(kp) of L, Lp. The group r is a special arithmetic group by definition if rp is a special maximal compact subgroup of G(kp) (in the sense of [5]) for