关于Berkovich环的缓和Anabel行为
Towards tempered anabelian behaviour of Berkovich annuli
摘要：
本文揭示了在布氏几何背景下解析环的某些部分\emph{anabelian behaviours}。更具体地说，如果$k$是一个代数闭的混合特征的赋值非阿基米德完全域，并且$\mathcal{C}_1$，$\mathcal{C}_2$是两个具有同构的调和基本群的$k$ -解析环，我们证明了$\mathcal{C}_1$和$\mathcal{C}_2$的长度不能相距太远.当他们是有限的，我们表明，他们的差异的绝对值是有界的上界仅取决于残留的特点$p$。
英文摘要：
This work brings to light some partial \emph{anabelian behaviours} of analytic annuli in the context of Berkovich geometry. More specifically, if $k$ is a valued non-archimedean complete field of mixed characteristic which is algebraically closed, and $\mathcal{C}_1$, $\mathcal{C}_2$ are two $k$-analytic annuli with isomorphic tempered fundamental group, we show that the lengths of $\mathcal{C}_1$ and $\mathcal{C}_2$ cannot be too far from each other. When they are finite, we show that the absolute value of their difference is bounded above with a bound depending only on the residual characteristic $p$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
