Summer School 2022 -  Cohomology, Geometry and Explicit number theory (COGENT)

Collection Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

Organizer(s) Institut Fourier, CNRS, UGA
Date(s) 13/06/2022 - 30/06/2022
linked URL https://if-summer2022.sciencesconf.org/
00:00:00 / 00:00:00
41 55

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

By Alexander, D. Rahm

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.

Information about the video

  • Date of recording 28/06/2022
  • Date of publication 03/12/2025
  • Institution Institut Fourier
  • Licence CC BY NC ND
  • Language English
  • Format MP4

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