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

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.

Luc Illusie, Yves Laszlo, Fabrice Orgogozo, editors. With the collaboration of Frederic Deglise, Alban Moreau, Vincent Pilloni, Michel Raynaud, Joel Riou, Benoit Stroh, and Michael Temkin. 416 pages. See http://www.math.polytechnique.fr/~orgogozo/travaux_de_Gabber/ for updates