论文标题
混合特征中刚性分析空间的可接受和de jong覆盖物之间的比较
Comparison between admissible and de Jong coverings of rigid analytic spaces in mixed characteristic
论文作者
论文摘要
如果$ k $是一个完整的非Archimedean字段和$ x $，则在$ \ Mathrm {spa}（k）$上本地的有限类型ADIC空间，令$ \ textbf {cov} _ {x} _ {x}^{\ mathrm {oc}}} $（desk。 $ \ textbf {cov} _ {x}^{\ mathrm {adm {adm}} $）是$ x $的étale覆盖物的类别，对于伯科维奇过度融合拓扑（可接收拓扑的分别），本地是本地的。有一个自然包含$ \ textbf {cov} _ {x}^{\ mathrm {oc}}} \ subseteq \ textbf {cov} _ {x}^}^{\ mathrm {adm {Amp}}} $。这个包容是否严格是De Jong最初提出的问题。 Achinger，Lara和Youcis的恢复工作中给出了一些部分答案。本说明的目的是表明，当$ k $具有混合特征$（0，p）$和$ p $ cluck时，此包含可能是严格的。结果，在Achinger，Lara和Youcis的工作之后，Noohi组的自然形态$π_1^{\ Mathrm {\ Mathrm {dj，\，\，Adm}}}}（x）\toπ_1^{\ Mathrm {dj，dj，\，oc}}}（x）（x）（x）（x）$不是一般的。
If $k$ is a complete non-archimedean field and $X$ an adic space locally of finite type over $\mathrm{Spa}(k)$, let $\textbf{Cov}_{X}^{\mathrm{oc}}$ (resp. $\textbf{Cov}_{X}^{\mathrm{adm}}$) be the category of étale coverings of $X$ that are locally for the Berkovich overconvergent topology (resp. for the admissible topology) disjoint union of finite étale coverings. There is a natural inclusion $\textbf{Cov}_{X}^{\mathrm{oc}}\subseteq \textbf{Cov}_{X}^{\mathrm{adm}}$. Whether or not this inclusion is strict is a question initially asked by de Jong. Some partial answers have been given in the recents works of Achinger, Lara and Youcis in the finite or equal characteristic $0$ cases. The purpose of this note is to show that this inclusion can be strict when $k$ is of mixed characteristic $(0,p)$ and $p$-closed. As a consequence, following the work of Achinger, Lara and Youcis, the natural morphism of Noohi groups $π_1^{\mathrm{dJ, \, adm}}(X)\to π_1^{\mathrm{dJ, \,oc}}(X)$ is not an isomorphism in general.
