We strengthen Gabber’s $l’$-alteration theorem by avoiding all primes invertible on a scheme. In particular, we prove that any scheme $X$ of finite type over a quasi-excellent threefold can be desingularized by a $\mathrm{char}(X)$-alteration, i.e., an alteration whose order is only divisible by primes noninvertible on $X$. The main new ingredient in the proof is a tame distillation theorem asserting that, after enlarging, any alteration of $X$ can be split into a composition of a tame Galois alteration and a $\mathrm{char}(X)$-alteration. The proof of the distillation theorem is based on the following tameness theorem that we deduce from a theorem of M. Pank: if a valued field $k$ of residue characteristic $p$ has no nontrivial $p$-extensions, then any algebraic extension $l/k$ is tame.
@article{10_4007_annals_2017_186_1_3,
author = {Michael Temkin},
title = {Tame distillation and desingularization by $p$-alterations},
journal = {Annals of mathematics},
pages = {97--126},
year = {2017},
volume = {186},
number = {1},
doi = {10.4007/annals.2017.186.1.3},
mrnumber = {3665001},
zbl = {06751219},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.186.1.3/}
}
TY - JOUR AU - Michael Temkin TI - Tame distillation and desingularization by $p$-alterations JO - Annals of mathematics PY - 2017 SP - 97 EP - 126 VL - 186 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.186.1.3/ DO - 10.4007/annals.2017.186.1.3 LA - en ID - 10_4007_annals_2017_186_1_3 ER -
Michael Temkin. Tame distillation and desingularization by $p$-alterations. Annals of mathematics, Tome 186 (2017) no. 1, pp. 97-126. doi: 10.4007/annals.2017.186.1.3
Cité par Sources :