Tame distillation and desingularization by p-alterations

• 成果类型: Article
• 署名作者: Temkin, Michael
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.186.1.3
• 发表日期: 2017
• 页码: 97-126
• 关键词: toric singularities; CURVES

摘要

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 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 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 1/k is tame.