Modular representations of GL(3, Fp), symmetric squares, and mod-p cohomology of GL(3, Z)

Avner Ash, Pham Huu Tiep

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We prove certain cases of nonabelian reciprocity between mod p Galois representations and Hecke eigenclasses in the mod p cohomology of GL(3,Z), using the symmetric square liftings from GL(2) and congruences on Hecke eigenvalues. We need to develop some modular representation theory for GL(3,Z/p). In some cases we also need to invoke certain computer calculations to finish the proof.

Original languageEnglish (US)
Pages (from-to)376-399
Number of pages24
JournalJournal of Algebra
Volume222
Issue number2
DOIs
StatePublished - Dec 15 1999

Keywords

  • Galois representations
  • Mod-p cohomology

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Modular representations of GL(3, F<sub>p</sub>), symmetric squares, and mod-p cohomology of GL(3, Z)'. Together they form a unique fingerprint.

  • Cite this