Some results about geometric Whittaker model

Roman Bezrukavnikov, Alexander Braverman, Ivan Mirkovic

Результат исследований: Вклад в журналСтатьярецензирование

14 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаАнглийский
Страницы (с-по)143-152
Число страниц10
ЖурналAdvances in Mathematics
Том186
Номер выпуска1
DOI
СостояниеОпубликовано - 1 авг. 2004
Опубликовано для внешнего пользованияДа

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