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

Abstract : 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.
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https://hal-upf.archives-ouvertes.fr/hal-02548734
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Submitted on : Monday, April 20, 2020 - 9:25:05 PM
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  • HAL Id : hal-02548734, version 1
  • ARXIV : 1708.02545

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Bui Anh Tuan, Alexander Rahm. Verification of the Quillen conjecture in the rank 2 imaginary quadratic case. Homology, Homotopy and Applications(HHA), International Press of Boston, Inc., 2017. ⟨hal-02548734⟩

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