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math.NT2015★ 20 cited
The codimension-one cohomology of SL_n Z
Thomas Church, Andrew Putman
We prove that H^{d-1}(SL_n Z; Q) = 0, where d = n-choose-2 is the cohomological dimension of SL_n Z, and similarly for GL_n Z. We also prove analogous vanishing theorems for cohomo…
math.NT2015★ 23 cited
Integrality in the Steinberg module and the top-dimensional cohomology of SL_n(O_K)
Thomas Church, Benson Farb, Andrew Putman
We prove a new structural result for the spherical Tits building attached to SL_n(K) for many number fields K, and more generally for the fraction fields of many Dedekind domains O…