Th\'eor\`eme de Gabber d'ind\'ependance de $l$

TL;DR

This paper discusses Gabber's theorem proving the independence of the prime number l for the intersection cohomology of proper equidimensional schemes over finite fields, following Fujiwara's approach closely.

Contribution

It provides a detailed presentation of Gabber's theorem on l-independence for intersection cohomology over finite fields, emphasizing the proof's structure and methodology.

Findings

Establishes l-independence of intersection cohomology for schemes over finite fields.

Clarifies the proof technique following Fujiwara's approach.

Reinforces the stability of intersection cohomology under change of l.

Abstract

We present Gabber's theorem of independence of $l$ for the intersection cohomology of a proper equidimensional scheme over the spectrum of a finite field. We follow [Fuji] very closely. ----- On expose ici le th\'eor\`eme de Gabber d'ind\'ependance de $l$ pour la cohomologie d'intersection d'un sch\'ema propre \'equidimensionnel sur le spectre d'un corps fini. On suit [Fuji] \`a tr\`es peu pr\`es.