Gabber’s work on local uniformization and étale cohomology of quasi-excellent schemes. Seminar at École Polytechnique 2006–2008. (Travaux de Gabber sur l’uniformisation locale et la cohomologie étale des schémas quasi-excellents. Séminaire à l’École Polytechnique 2006–2008.) (French, English) Zbl 1297.14003

Astérisque 363-364. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-790-2/pbk). xxi, 525 p. (2014).

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The articles of this volume will be reviewed individually.
Indexed articles:
Raynaud, Michel; Laszlo, Yves, Exposé I. Excellent rings, 1-19 [Zbl 1320.13025]
Orgogozo, Fabrice, Exposé II. Topologies adapted to local uniformization, 21-36 [Zbl 1320.14004]
Illusie, Luc; Laszlo, Yves, Exposé III. Approximation, 37-49 [Zbl 1320.13012]
Orgogozo, Fabrice, Exposé IV. The Cohen-Gabber theorem, 51-68 [Zbl 1320.13004]
Orgogozo, Fabrice, Exposé V. Partial algebraization, 69-75 [Zbl 1320.13022]
Illusie, Luc, Exposé VI. Log regularity, very tame actions, 77-97 [Zbl 1320.14062]
Orgogozo, Fabrice, Exposé VII. Proof of the (weak) local minimization theorem, 99-101 [Zbl 1320.14021]
Gabber, Ofer, Appendix A. Facsimile: A finiteness theorem for non abelian \(H^1\) of excellent schemes., A1-A19 [Zbl 1320.14025]
Gabber, Ofer, Appendix B. Facsimile: Finiteness theorem for étale cohomology of excellent schemes., B1-B27 [Zbl 1320.14037]
Illusie, Luc; Temkin, Michael, Exposé VIII. Gabber’s modification theorem (absolute case), 103-160 [Zbl 1327.14071]
Illusie, Luc, Exposé IX. Local uniformization prime to \(\ell\), 161-165 [Zbl 1320.14020]
Illusie, Luc; Temkin, Michael, Exposé X. Gabber’s modification theorem (log smooth case), 167-212 [Zbl 1327.14072]
Illusie, Luc, Exposé XI. Oriented products, 213-234 [Zbl 1320.18003]
Orgogozo, Fabrice, Exposé XII\(_A\). Oriented cohomological descent, 235-249 [Zbl 1320.14005]
Zheng, Weizhe, Exposé XII\(_B\). On hyper base change, 251-260 [Zbl 1320.14009]
Orgogozo, Fabrice, Exposé XIII. The finiteness theorem, 261-275 [Zbl 1320.14006]
Pilloni, Vincent; Stroh, Benoît, Exposé XIV. Dimension functions, 277-292 [Zbl 1320.14007]
Pilloni, Vincent; Stroh, Benoît, Exposé XV. The affine Lefschetz theorem, 293-300 [Zbl 1320.14008]
Riou, Joël, Exposé XVI. Chern classes, Gysin morphisms, absolute purity, 301-349 [Zbl 1320.14031]
Riou, Joël, Exposé XVII. Duality, 351-453 [Zbl 1320.14032]
Illusie, Luc, Exposé XVIII\(_A\). Cohomological dimension: first results, 455-459 [Zbl 1320.14026]
Orgogozo, Fabrice, Exposé XVIII\(_B\). Cohomological dimension: refinements and complements, 461-480 [Zbl 1320.14030]
Laszlo, Yves, Exposé XIX. A counter-example, 481-490 [Zbl 1320.14027]
Laszlo, Yves; Moreau, Alban, Exposé XX. Rigidity., 491-528 [Zbl 1320.14028]
Déglise, Frédéric, Exposé XXI. The finiteness theorem for nonabelian coefficients., 529-553 [Zbl 1320.14024]
Illusie, Luc; Laszlo, Yves; Orgogozo, Fabrice, Introduction, xiii-xix [Zbl 1320.14002]

MSC:

14-06	Proceedings, conferences, collections, etc. pertaining to algebraic geometry
13-06	Proceedings, conferences, collections, etc. pertaining to commutative algebra
14F20	Étale and other Grothendieck topologies and (co)homologies
14L30	Group actions on varieties or schemes (quotients)
13B40	Étale and flat extensions; Henselization; Artin approximation
13F40	Excellent rings
00B25	Proceedings of conferences of miscellaneous specific interest