通过$p$ -改变驯服蒸馏和去奇异化
Tame distillation and desingularization by $p$-alterations
摘要：
通过避免一个方案上所有可逆素数的存在，加强了Gabber的$l'$ -变换定理.特别地，我们证明了在拟优三重上的任何有限型方案$X$都可以被一个$\mathrm{char}(X)$ -变换去奇异化，即一个变换的阶只能被$X$上不可逆的素数整除.证明中的主要新成分是一个驯服蒸馏定理，该定理断言，在扩大后，$X$的任何改变都可以分解为驯服伽罗瓦改变和$\mathrm{char}(X)$ -改变的组合。蒸馏定理的证明是基于下面的驯服定理，我们从M. Pank：如果剩余特征$p$的值域没有非平凡的$p$ -扩张，则它的任何代数扩张都是驯服的。
英文摘要：
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 $\mathrm{char}(X)$-alteration, i.e. an alteration whose order is only divisible by primes non-invertible 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 of residue characteristic $p$ has no non-trivial $p$-extensions then any its algebraic extension is tame.
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