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Local Fourier transform and epsilon factors

Part of: Algebraic number theory: local and $p$-adic fields (Co)homology theory

Published online by Cambridge University Press:  05 August 2010

Ahmed Abbes  and
Takeshi Saito
Ahmed Abbes
Affiliation:
CNRS UMR 6625, IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France (email: ahmed.abbes@univ-rennes1.fr)
Takeshi Saito
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan (email: t-saito@ms.u-tokyo.ac.jp)
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Abstract

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Laumon introduced the local Fourier transform for ℓ-adic Galois representations of local fields, of equal characteristic p different from ℓ, as a powerful tool for studying the Fourier–Deligne transform of ℓ-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 ε-factor to the determinant of the local Fourier transform under the same condition.

Keywords

local Fourier transformε-factorsramificationvanishing cyclesArtin–Schreier–Witt theory

MSC classification

Secondary: 14F20: Étale and other Grothendieck topologies and (co)homologies 11S15: Ramification and extension theory
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 6 , November 2010 , pp. 1507 - 1551
Copyright
Copyright © Foundation Compositio Mathematica 2010

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