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 FourierDeligne 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2008
 DOI:
 10.48550/arXiv.0809.0180
 arXiv:
 arXiv:0809.0180
 Bibcode:
 2008arXiv0809.0180A
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14F20;
 11S15
 EPrint:
 Compositio Mathematica, 1466, (2010) 15071551