Mod 2 homology for GL(4) and Galois representations

Avner Ash, Paul E. Gunnells, Mark McConnell

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We extend the computations in [AGM11] to find the mod 2 homology in degree 1 of a congruence subgroup Γ of SL(4,Z) with coefficients in the sharbly complex, along with the action of the Hecke algebra. This homology group is related to the cohomology of Γ with F2 coefficients in the top cuspidal degree. These computations require a modification of the algorithm to compute the action of the Hecke operators, whose previous versions required division by 2. We verify experimentally that every mod 2 Hecke eigenclass found appears to have an attached Galois representation, giving evidence for a conjecture in [AGM11]. Our method of computation was justified in [AGM12].

Original languageEnglish (US)
Pages (from-to)4-22
Number of pages19
JournalJournal of Number Theory
Volume146
Issue numberC
DOIs
StatePublished - 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Cohomology of arithmetic groups
  • Galois representations
  • Modular symbols
  • Primary
  • Secondary
  • Steinberg module
  • Voronoi complex

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