Anh Tuan, Bui; Rahm, Alexander D. Verification of the Quillen conjecture in the rank 2 imaginary quadratic case. (English) Zbl 1440.11088 Homology Homotopy Appl. 22, No. 2, 265-278 (2020). Summary: We confirm a conjecture of Quillen in the case of the \(\operatorname{mod} 2\) cohomology of arithmetic groups \(\mathrm{SL}_2(\mathcal{O}_{\mathbb{Q}(\sqrt{-m})}[\frac{1}{2}])\), where \(\mathcal{O}_{\mathbb{Q}(\sqrt{-m})}\) is an imaginary quadratic ring of integers. To make explicit the free module structure on the cohomology ring conjectured by Quillen, we compute the \(\operatorname{mod} 2\) cohomology of \(\text{SL}_2(\mathbb{Z}[\sqrt{-2}][\frac{1}{2}])\) via the amalgamated decomposition of the latter group. MSC: 11F75 Cohomology of arithmetic groups Keywords:cohomology of arithmetic groups PDFBibTeX XMLCite \textit{B. Anh Tuan} and \textit{A. D. Rahm}, Homology Homotopy Appl. 22, No. 2, 265--278 (2020; Zbl 1440.11088) Full Text: DOI arXiv