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Exposé X. Gabber’s modification theorem (log smooth case). (English) Zbl 1327.14072

Illusie, Luc (ed.) et al., Travaux de Gabber sur l’uniformisation locale et la cohomologie étale des schémas quasi-excellents. Séminaire à l’École Polytechnique 2006–2008. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-790-2/pbk). Astérisque 363-364, 167-212 (2014).
From the text: We state and prove a variant of the main theorem of VIII (see VIII–1.1) for schemes \(X\) which are log smooth over a base \(S\) with trivial \(G\)-action. See 1.1 for a precise statement. The proof is given in §1 and in the remaining part of the expose we deduce refinements of classical theorems of de Jong, for schemes of finite type over a field or a trait, where the degree of the alteration is made prime to a prime \(\ell\) invertible on the base. Sections 2 and 3 are independent and contain two different proofs of such a refinement.
For the entire collection see [Zbl 1297.14003].

MSC:

14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14L30 Group actions on varieties or schemes (quotients)
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