Ahmed Abbes

Ramification of local fields with imperfect residue fields

We define two decreasing filtrations by ramification groups on the absolute Galois group of a complete discrete valuation field whose residue field may not be perfect. In the classical case where the residue field is perfect, we recover the classical upper numbering filtration. The definition uses rigid geometry and log-structures. We also establish some of their properties.

The characteristic class and ramification of an ℓ-adic étale sheaf

We introduce the characteristic class of an ℓ-adic étale sheaf using a cohomological pairing due to Verdier (SGA5). As a consequence of the Lefschetz–Verdier trace formula, its trace computes the Euler–Poincaré characteristic of the sheaf. We compare the characteristic class to two other invariants arising from ramification theory. One is the Swan class of Kato-Saito [17] and the other is the 0-cycle class defined by Kato for rank 1 sheaves in [16].

Local Fourier transform and epsilon factors

Laumon introduced the local Fourier transform for

Cycles on Arithmetic Surfaces

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Chapter I. Representations of the fundamental group and the torsor of deformations. An overview

-adic Galois representations of local fields, of equal characteristic

Espaces rigides quasi-séparés

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Invariants différentiels. Morphismes lisses

different from

À propos de la conjecture de Manin pour les courbes elliptiques modulaires

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Sous-groupes canoniques et cycles évanescents p-adiques pour les variétés abéliennes

, as a powerful tool to study the Fourier-Deligne transform of

Comparaison des métriques d’Arakelov et de Poincaré sur

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