Publication Date

2004

Journal or Book Title

ADVANCES IN MATHEMATICS

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 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 -equivariant sheaves on X where 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.

Comments

This is the pre-published version harvested from arXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6W9F-49Y994B-1&_user=1516330&_coverDate=08%2F01%2F2004&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1663903777&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=66d8da02effc74cc19cbe8d38379a2d4&searchtype=a

Pages

143-152

Volume

186

Issue

1

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