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- W1968024712 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→Ga 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." @default.
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- W1968024712 date "2004-08-01" @default.
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- W1968024712 title "Some results about geometric Whittaker model" @default.
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- W1968024712 doi "https://doi.org/10.1016/j.aim.2003.07.011" @default.
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