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

Research output: Contribution to journal › Article › peer-review

6 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
Externally published	Yes

Keywords

Galois representations
Mod-p cohomology

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1006/jabr.1999.7988

Cite this

@article{a43b97361f31497989e6a1e98f5000bb,

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

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.",

keywords = "Galois representations, Mod-p cohomology",

author = "Avner Ash and Tiep, \{Pham Huu\}",

note = "Funding Information: * The first author was supported in part by NSA Grant MDA-904-94-2030 and NSF Grant DMS-9531675. †Part of this work was done while the second author was participating in the special semester on Representations of Algebraic Groups and Related Finite Groups at the Isaac Newton Institute (Cambridge). It is a pleasure to thank the Institute for its hospitality. ‡The authors are grateful to S. Doty, R. Taylor, G. Walker, and B. Mazur for helpful discussions.",

year = "1999",

month = dec,

day = "15",

doi = "10.1006/jabr.1999.7988",

language = "English (US)",

volume = "222",

pages = "376--399",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Modular representations of GL(3, Fp), symmetric squares, and mod-p cohomology of GL(3, Z)

AU - Ash, Avner

AU - Tiep, Pham Huu

N1 - Funding Information: * The first author was supported in part by NSA Grant MDA-904-94-2030 and NSF Grant DMS-9531675. †Part of this work was done while the second author was participating in the special semester on Representations of Algebraic Groups and Related Finite Groups at the Isaac Newton Institute (Cambridge). It is a pleasure to thank the Institute for its hospitality. ‡The authors are grateful to S. Doty, R. Taylor, G. Walker, and B. Mazur for helpful discussions.

PY - 1999/12/15

Y1 - 1999/12/15

N2 - 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.

AB - 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.

KW - Galois representations

KW - Mod-p cohomology

UR - https://www.scopus.com/pages/publications/0033573010

UR - https://www.scopus.com/pages/publications/0033573010#tab=citedBy

U2 - 10.1006/jabr.1999.7988

DO - 10.1006/jabr.1999.7988

M3 - Article

AN - SCOPUS:0033573010

SN - 0021-8693

VL - 222

SP - 376

EP - 399

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -