On arithmetically defined hyperbolic 5-manifolds arising from maximal orders in definite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e28" altimg="si17.svg"><mml:mi mathvariant="double-struck">Q</mml:mi></mml:math>-

Using the quaternionic formalism for the description of the group of isometries of hyperbolic 5-space we consider arithmetically defined 5-dimensional hyperbolic manifolds which are non-compact but of finite volume. They arise from maximal orders Λ in the central simple algebra M 2 ( D ) of degree 4 where D denotes a definite quaternion Q -algebra. The affine Z -group scheme S L Λ determines an integral structure for the algebraic Q -group G = S L Λ × Z Q obtained by base change. The group G is an inner form of the special linear Q -group S L 4 . Each torsion-free subgroup Γ ⊂ S L Λ ( Z ) determines a hyperbolic 5-manifold, to be denoted X G / Γ . Given a principal congruence subgroup Γ ( p e ) , we determine the number of ends and the dimensions of the cohomology groups at infinity of the manifold X G / Γ ( p e ) .