论文标题
完美域字段的标准
A criterion for perfectoid fields
论文作者
论文摘要
倾斜对应关系是完美域中的基本属性。在本说明中，我们表明，倾斜结构也可用于检测非架构的田地之间的完美域。特别是，对于$ k $，$ \ mathbb {c} _p $的完整子字段（$ \ mathbb {q} _p $）的完整代数闭合$ \ mathbb {q} _p $），$ k $是完美的，并且仅当其倾斜度不超过$ \ mathbb {f} f} _p _p $。我们还包括有关APF（算术上的）扩展，完美域及其关系的一些猜想。
The tilting correspondence is a fundamental property of perfectoid fields. In this note, we show that the tilting construction can also be used to detect perfectoid fields among nonarchimedean fields. In particular, for $K$ a complete subfield of $\mathbb{C}_p$ (a completed algebraic closure of $\mathbb{Q}_p$), $K$ is perfectoid if and only if its tilt is not algebraic over $\mathbb{F}_p$. We also include some conjectures on APF (arithmetically profinite) extensions, perfectoid fields, and their relations.
