Torsion in the cohomology of congruence subgroups of SL(4,Z) and Galois representations

Avner Ash, Paul E. Gunnells, Mark McConnell

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We report on the computation of torsion in certain homology theories of congruence subgroups of SL(4,Z). Among these are the usual group cohomology, the Tate-Farrell cohomology, and the homology of the sharbly complex. All of these theories yield Hecke modules. We conjecture that the Hecke eigenclasses in these theories have attached Galois representations. The interpretation of our computations at the torsion primes 2, 3, 5 is explained. We provide evidence for our conjecture in the 15 cases of odd torsion that we found in levels ≤31.

Original languageEnglish (US)
Pages (from-to)404-415
Number of pages12
JournalJournal of Algebra
Issue number1
StatePublished - Jan 1 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Automorphic forms
  • Cohomology of arithmetic groups
  • Galois representations
  • Hecke operators
  • Primary
  • Secondary
  • Torsion cohomology classes


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