Taking place at Université Pierre et Marie Curie, 8th of June, 2017.

Hans-Werner Henn (Université de Strasbourg)

## On the mod-2 cohomology of SL_3(**Z**[1/2,i])

Let Gamma = SL_3(**Z**[1/2,i]), let *X* be any mod-2 acyclic Gamma-CW complex
on which Gamma acts with finite stabilizers, e.g. the product of the
symmetric space for
SL(3,**Z**[i]) and the Bruhat-Tits building for SL_3(**Q**_2[i]), and let *X_s* be
the
2-singular locus of *X*. We explain how to calculate the mod-2 cohomology
of the Borel construction of *X_s*
with respect to the action of Gamma. This cohomology coincides with the
mod-2 cohomology
of Gamma in cohomological degrees bigger than 8; and the result is
compatible with a conjecture of
Quillen which predicts the strucure of the cohomology ring
H*(Gamma; **Z**/2).

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