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 journal › Article

5 Citations (Scopus)

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
StatePublished - Dec 15 1999
Externally publishedYes

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Modular Representations
Galois Representations
Reciprocity
Representation Theory
Congruence
Cohomology
Eigenvalue

Keywords

  • Galois representations
  • Mod-p cohomology

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Modular representations of GL(3, Fp), symmetric squares, and mod-p cohomology of GL(3, Z). / Ash, Avner; Tiep, Pham Huu.

In: Journal of Algebra, Vol. 222, No. 2, 15.12.1999, p. 376-399.

Research output: Contribution to journal › Article

Ash, A & Tiep, PH 1999, 'Modular representations of GL(3, Fp), symmetric squares, and mod-p cohomology of GL(3, Z)', Journal of Algebra, vol. 222, no. 2, pp. 376-399.
Ash A, Tiep PH. Modular representations of GL(3, Fp), symmetric squares, and mod-p cohomology of GL(3, Z). Journal of Algebra. 1999 Dec 15;222(2):376-399.
Ash, Avner ; Tiep, Pham Huu. / Modular representations of GL(3, Fp), symmetric squares, and mod-p cohomology of GL(3, Z). In: Journal of Algebra. 1999 ; Vol. 222, No. 2. pp. 376-399.
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