## Abstract

In this note I will describe our joint work with David Kazhdan on the global Langlands correspondence over function fields for arbitrary split reductive groups.

Our main result asserts that for every pair (π,ω), where π is a cuspidal representation of G one of whose local components is a cuspidal Deligne-Lusztig representation, and ω is a representation of the dual group, there exists a virtual Galois representation ρπ,ω, whose L-function equals the L-function of the pair (π,ω).

Our main result asserts that for every pair (π,ω), where π is a cuspidal representation of G one of whose local components is a cuspidal Deligne-Lusztig representation, and ω is a representation of the dual group, there exists a virtual Galois representation ρπ,ω, whose L-function equals the L-function of the pair (π,ω).

Original language | English |
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Title of host publication | Symmetries in algebra and number theory (SANT) |

Publisher | Universitätsverlag Göttingen, Göttingen |

Pages | 139-147 |

Number of pages | 9 |

ISBN (Print) | 978-3-940344-96-0 |

State | Published - 2009 |

Event | Symmetries in Algebra and Number Theory : Göttingen-Jerusalem conference - Göttingen, Germany Duration: 27 Oct 2008 → 30 Oct 2008 |

### Conference

Conference | Symmetries in Algebra and Number Theory |
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Abbreviated title | SANT |

Country/Territory | Germany |

City | Göttingen |

Period | 27/10/08 → 30/10/08 |