## Abstract

Let G be an algebraic reductive group over a field of positive characteristic. Choose a parabolic subgroup P in G and denote by U its unipotent radical. Let X be a G-variety. The purpose of this paper is to give two examples of a situation in which the functor of averaging of ℓ-adic sheaves on X with respect to a generic character χ:U→G_{a} commutes with Verdier duality. Namely, in the first example we take X to be an arbitrary G-variety and we prove the above property for all U-equivariant sheaves on X where U is the unipotent radical of an opposite parabolic subgroup; in the second example we take X=G and we prove the corresponding result for sheaves which are equivariant under the adjoint action (the latter result was conjectured by B. C. Ngo who proved it for G=GL(n)). As an application of the proof of the first statement we reprove a theorem of N. Katz and G. Laumon about local acyclicity of the kernel of the Fourier-Deligne transform.

Original language | English |
---|---|

Pages (from-to) | 143-152 |

Number of pages | 10 |

Journal | Advances in Mathematics |

Volume | 186 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Aug 2004 |

Externally published | Yes |

## Keywords

- Fourier-Deligne transform
- Reductive groups
- Whittaker model