Constructs a projective resolution of the symplectic Steinberg module St^ω_{2n}(K) and uses it to compute top cohomology of level-p congruence subgroups of Sp_{2n}(R) for Euclidean R with surjective unit map.
Commentarii Mathematici Helvetici , volume=
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For Euclidean rings R and prime p, the top cohomology H^ν(Γ_n(p)) of level-p congruence subgroups of SL_n(R) maps surjectively to the reduced homology of the Tits building quotient, with conditions for isomorphism.
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A projective resolution of the symplectic Steinberg module
Constructs a projective resolution of the symplectic Steinberg module St^ω_{2n}(K) and uses it to compute top cohomology of level-p congruence subgroups of Sp_{2n}(R) for Euclidean R with surjective unit map.
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The top cohomology of principal congruence subgroups of special linear groups over Euclidean number rings
For Euclidean rings R and prime p, the top cohomology H^ν(Γ_n(p)) of level-p congruence subgroups of SL_n(R) maps surjectively to the reduced homology of the Tits building quotient, with conditions for isomorphism.