A new Fourier transform

@article{Wang2014ANF,
  title={A new Fourier transform},
  author={Jonathan Wang},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
  • Jonathan Wang
  • Published 22 February 2014
  • Mathematics
  • arXiv: Algebraic Geometry
In order to define a geometric Fourier transform, one usually works with either $\ell$-adic sheaves in characteristic $p>0$ or with $D$-modules in characteristic 0. If one considers $\ell$-adic sheaves on the stack quotient of a vector bundle $V$ by the homothety action of $\mathbb{G}_m$, however, Laumon provides a uniform geometric construction of the Fourier transform in any characteristic. The category of sheaves on $[V/\mathbb{G}_m]$ is closely related to the category of (unipotently… 
An Iwahori-Whittaker model for the Satake category
In this paper we prove, for G a connected reductive algebraic group satisfying a technical assumption, that the Satake category of G (with coefficients in a finite field, a finite extension of Q_l,

References

SHOWING 1-10 OF 12 REFERENCES
On Koszul duality for Kac-Moody groups
For any Kac-Moody group $G$ with Borel $B$, we give a monoidal equivalence between the derived category of $B$-equivariant mixed complexes on the flag variety $G/B$ and (a certain completion of) the
How to glue perverse sheaves
The aim of this note [0] is to give a short, self-contained account of the vanishing cycle constructions of perverse sheaves; e.g., for the needs of [1]. It differs somewhat from the alternative
The Weil conjectures
In discussing the question of rational points on algebraic curves, we are usually concerned with Q. Andre Weil looked instead at curves over finite fields; assembling the counts into a function, he
Compact generation of the category of D-modules on the stack of G-bundles on a curve
The goal of the paper is to show that the (derived) category of D-modules on the stack Bun_G(X) is compactly generated. Here X is a smooth complete curve, and G is a reductive group. The problem is
Transformation de Fourier homogène
Dans leur demonstration de la correspondance de Drinfeld-Langlands, Frenkel, Gaitsgory et Vilonen utilisent la transformation de Fourier geometrique, ce qui les oblige a travailler soit avec les
Astérisque
  • (130):218–236,
  • 1985
Spécialisation de faisceaux et monodromie modérée
  • Analysis and topology on singular spaces, II, III (Luminy, 1981), volume 101 of Astérisque, pages 332–364. Soc. Math. France, Paris
  • 1983
...
...