论文标题
通过倾斜对应关系的可决定性
Decidability via the tilting correspondence
论文作者
论文摘要
我们证明了完美素场的相对可决定性结果。这适用于表明字段$ \ mathbb {q} _p（p^{1/p^{\ infty}}）$和$ \ mathbb {q} _p（ζ_{p^{p^{\ infty}}） \ Mathbb {f} _p（\！（t）\！）$和$ \ Mathbb {q} _p^{ab} $是（存在的）相对于$ \ offline的完美船体{\ superline {\ mathbb {f}} _ p（\！\！（t）\！）$。我们还证明了一些无条件的可确定性会导致混合特征通过减少到特征$ p $。
We prove a relative decidability result for perfectoid fields. This applies to show that the fields $\mathbb{Q}_p(p^{1/p^{\infty}})$ and $\mathbb{Q}_p(ζ_{p^{\infty}})$ are (existentially) decidable relative to the perfect hull of $ \mathbb{F}_p(\!(t)\!)$ and $\mathbb{Q}_p^{ab}$ is (existentially) decidable relative to the perfect hull of $\overline{ \mathbb{F}}_p(\!(t)\!)$. We also prove some unconditional decidability results in mixed characteristic via reduction to characteristic $p$.
