### Abstract

Conjecturally, by the Langlands philosophy, a cuspidal cohomology class of level N for SL(n, ℤ) should have an attached Galois representation. This is a finite-dimensional l-adic representation π of Gal(ℚ/ℚ), unramified for primes p not dividing l and N, for which the image of a Frobenius element for p is related to the p-th Hecke eigenvalues of the class. By a conjecture of Ash [1], the same should hold for l-torsion cohomology classes α.

Original language | English (US) |
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Title of host publication | Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings |

Editors | Leonard M. Adleman, Ming-Deh Huang |

Publisher | Springer Verlag |

ISBN (Print) | 9783540586913 |

DOIs | |

State | Published - Jan 1 1994 |

Externally published | Yes |

Event | 1st Algorithmic Number Thoery Symposium, ANTS-I 1994 - Ithaca, United States Duration: May 6 1994 → May 9 1994 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 877 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 1st Algorithmic Number Thoery Symposium, ANTS-I 1994 |
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Country | United States |

City | Ithaca |

Period | 5/6/94 → 5/9/94 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Galois representations and Cohomology of SL(3, ℤ)'. Together they form a unique fingerprint.

## Cite this

McConnell, M. (1994). Galois representations and Cohomology of SL(3, ℤ). In L. M. Adleman, & M-D. Huang (Eds.),

*Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings*(Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 877 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-58691-1_51