## 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) |
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Pages (from-to) | 376-399 |

Number of pages | 24 |

Journal | Journal of Algebra |

Volume | 222 |

Issue number | 2 |

DOIs | |

State | Published - Dec 15 1999 |

Externally published | Yes |

## Keywords

- Galois representations
- Mod-p cohomology

## ASJC Scopus subject areas

- Algebra and Number Theory

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