Verification of the Quillen conjecture in the rank 2 imaginary quadratic case

Bui Anh Tuan , Alexander D. Rahm (1)

1 GAATI - Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information

We confirm a conjecture of Quillen in the case of the mod 2 coho-mology of arithmetic groups SL2(O Q(√ −m) [ 1 2 ]), where O Q(√ −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 mod 2 cohomology of SL2(Z[ √ −2 ][ 1 2 ]) via the amalgamated decomposition of the latter group.

Domaines: Topologie algébrique [math.AT]

Bui Anh Tuan, Alexander D. Rahm. Verification of the Quillen conjecture in the rank 2 imaginary quadratic case. Homology, Homotopy and Applications(HHA), 2017, 22 (2), ⟨10.4310/HHA.2020.v22.n2.a17⟩. ⟨hal-02548734⟩