### 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 |

State | Published - Dec 15 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Galois representations
- Mod-p cohomology

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

_{p}), symmetric squares, and mod-p cohomology of GL(3, Z).

*Journal of Algebra*,

*222*(2), 376-399.

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

Research output: Contribution to journal › Article

_{p}), symmetric squares, and mod-p cohomology of GL(3, Z)',

*Journal of Algebra*, vol. 222, no. 2, pp. 376-399.

_{p}), symmetric squares, and mod-p cohomology of GL(3, Z). Journal of Algebra. 1999 Dec 15;222(2):376-399.

}

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

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 - http://www.scopus.com/inward/record.url?scp=0033573010&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033573010&partnerID=8YFLogxK

M3 - Article

VL - 222

SP - 376

EP - 399

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -