Mathematics – Algebraic Geometry
Scientific paper
2002-10-16
Mathematics
Algebraic Geometry
8 pages
Scientific paper
Let G be an algebraic reductive group over a an algebraically closed 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 of U 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 $\oU$-equivariant sheaves on X where $\oU$ 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)). Analogous results hold also for D-modules when k is replaced by the field of complex numbers. 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.
Bezrukavnikov Roman
Braverman Alexander
Mirkovic Ivan
No associations
LandOfFree
Some results about the geometric Whittaker model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Some results about the geometric Whittaker model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some results about the geometric Whittaker model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-569683