# Local Fourier transform and epsilon factors

Abstract : Laumon introduced the local Fourier transform for $\ell$-adic Galois representations of local fields, of equal characteristic $p$ different from $\ell$, as a powerful tool to study the Fourier-Deligne transform of $\ell$-adic sheaves over the affine line. In this article, we compute explicitly the local Fourier transform of monomial representations satisfying a certain ramification condition, and deduce Laumon's formula relating the epsilon factor to the determinant of the local Fourier transform under the same condition.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00374041
Contributor : Marie-Annick Guillemer <>
Submitted on : Tuesday, April 7, 2009 - 5:19:40 PM
Last modification on : Friday, November 16, 2018 - 1:24:34 AM

### Citation

Ahmed Abbes, Takeshi Saito. Local Fourier transform and epsilon factors. Compositio Mathematica, Foundation Compositio Mathematica, 2010, 146 (6), pp.1507-1551. 〈10.1112/s0010437x09004631〉. 〈hal-00374041〉

Record views