Volume: 363; 2014; 619 pp; Softcover
MSC: Primary 12; 13; 14; 18; 20;
Print ISBN: 978-2-85629-790-2
Product Code: AST/363/364
List Price: $210.00
Individual Member Price: $168.00
Travaux de Gabber sur L’uniformisation Locale et la Cohomologie Étale des Schémas Quasi-ExcellentsShare this page
Edited by Luc Illusie; Yves Laszlo; Fabrice Orgogozo
with the collaboration of F. Déglise, A. Morau, V. Pilloni, M. Raynaud, J. Riou, B. Stroh, M. Temkin, and W. Zheng
A publication of the Société Mathématique de France
The work of Ofer Gabber presented in this book can be roughly divided into two closely related parts: a geometric one and a cohomological one. The first part contains local uniformization theorems which state that any pair consisting of a quasi-excellent noetherian scheme and a nowhere dense closed subscheme becomes isomorphic, after localization by suitable étale morphisms and alterations, to a pair consisting of a regular scheme and a normal crossings divisor. These are local results, but their proofs have global theorems as corollaries, refining alteration theorems of de Jong for schemes of finite type over a field or a Dedekind ring. Techniques from logarithmic geometry and, concerning the finest results, canonical desingularization in characteristic zero, play a key role in the proofs.
In the second part, the book gives applications, with examples and counterexamples, to abelian finiteness theorems, as well as theorems on cohomological dimension and duality in étale cohomology over quasi-excellent schemes. In particular, Grothendieck's local duality conjecture is proved, and his absolute cohomological purity conjecture is proved by a new method. Non-abelian rigidity and finiteness results are also established in the final exposés.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Table of Contents
Table of Contents
Travaux de Gabber sur L'uniformisation Locale et la Cohomologie Etale des Schemas Quasi-Excellents
Graduate students and research mathematicians.