Travaux de Gabber sur l'uniformisation locale et la cohomologie etale des schemas quasi-excellents. Seminaire a l'Ecole polytechnique 2006--2008

TL;DR

This seminar notes Gabber's groundbreaking work on etale cohomology and uniformization of quasi-excellent schemes, covering constructibility, vanishing, uniformization, rigidity, and duality results that advance algebraic geometry.

Contribution

It presents new proofs and results on etale cohomology, including constructibility, vanishing, and uniformization theorems for quasi-excellent schemes, with applications to purity and duality.

Findings

Proved constructibility theorems for etale cohomology.

Established vanishing theorems like affine Lefschetz.

Developed uniformization for the prime-to-l alteration topology.

Abstract

This book contains notes of a seminar on Ofer Gabber's work on the etale cohomology and uniformization of quasi-excellent schemes. His main results include (cf. introduction) constructibility theorems (for abelian or non-abelian coefficients), vanishing theorems (e.g. affine Lefschetz), uniformization for the "prime-to-l alteration topology", rigidity for non-abelian coefficients, a new proof of the absolute purity conjecture, duality, etc.