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

Avner Ash; Pham Huu Tiep

doi:10.1006/jabr.1999.7988

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

Avner Ash, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article

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 language	English (US)
Pages (from-to)	376-399
Number of pages	24
Journal	Journal of Algebra
Volume	222
Issue number	2
DOIs	https://doi.org/10.1006/jabr.1999.7988
State	Published - Dec 15 1999

Keywords

Galois representations
Mod-p cohomology

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1006/jabr.1999.7988

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Ash, A., & Tiep, P. H. (1999). Modular representations of GL(3, F_p), symmetric squares, and mod-p cohomology of GL(3, Z). Journal of Algebra, 222(2), 376-399. https://doi.org/10.1006/jabr.1999.7988

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