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Vidéo Année : 2022

Alexander RAHM - Verification of the Quillen conjecture in the rank 2 imaginary quadratic case

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Alexander D. Rahm
Fanny Bastien

Résumé

We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL(2, A[1/2]), where A 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 SL(2, B[1/2]) with B the imaginary quadratic ring of discriminant -8 (obtained as the ring of integers from the imaginary quadratic field generated by the square-root of -2) via the amalgamated decomposition of the latter group. This is joint work with Tuan Anh Bui.

Dates et versions

hal-04662996 , version 1 (26-07-2024)

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  • HAL Id : hal-04662996 , version 1

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Alexander D. Rahm, Fanny Bastien. Alexander RAHM - Verification of the Quillen conjecture in the rank 2 imaginary quadratic case: Summer School 2022 - Cohomology, Geometry and Explicit Number Theory. 2022. ⟨hal-04662996⟩
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