发表机构
Peking University; Chinese Academy of Sciences（北京大学; 中国科学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了一个在$\mathbb C_p$上的光滑连通刚性解析曲线及其完美拟平展$\mathbb Z_p^2$-环，其几何Sen态射非满射，否证了Rodríguez Camargo的猜想，并依赖拉回定理保持完美塔。
AI 中文摘要
我们构造了在$\mathbb C_p$上的一条光滑连通的刚性解析曲线，它带有一个仿射完美拟平展$\mathbb Z_p^2$-环，其几何Sen态射不是满射，从而否证了Rodr\\'iguez Camargo关于完美性蕴含满射性的猜想。该构造依赖于一个拉回定理，该定理表明在刚性解析空间的泛单射态射下，完美拟平展塔得以保持。
英文摘要
We study surjectivity of the geometric Sen map for perfectoid $G$-torsors over smooth rigid analytic spaces over $\mathbb{C}_p$, where $G$ is a compact $p$-adic Lie group. We construct an affinoid perfectoid $\mathbb{Z}_p^2$-torsor over a smooth curve whose Sen map is not surjective, thereby disproving Rodríguez Camargo's conjectured implication from perfectoidness to surjectivity. We prove that the Sen map of every perfectoid $G$-torsor over a smooth curve is nevertheless surjective on a Zariski open dense subset. Finally, we show that locally analytic decompletion implies Sen surjectivity for diamondian affinoid perfectoid torsors.
