AI 中文总结
本文针对素数p和特征p的完美仿射域K，构造了带C_p作用的几何正规次完美仿射拓扑空间，其v环空间范畴的商非仿射，表明仿射完美空间的有限商稳定性不适用于次完美空间。
AI 中文摘要
对每个素数p和每个特征p的完美仿射域K，我们构造一个具有C_p作用的几何正规次完美仿射拓扑空间，其在v环空间范畴中的商不是仿射的。该源是稳定一致且层化的，而在不动点处的共尾有理邻域序列获得了新的一阶不变截面，这些截面无法通过完备有理局部化下降。因此，仿射完美空间的有限商稳定性不能推广到次完美空间。
英文摘要
For every prime $p$ and every perfectoid field $K$ of characteristic $p$, we construct a geometrically normal sousperfectoid affinoid adic space with a $C_p$-action whose quotient in the category of $v$-ringed spaces is not adic. The source is stably uniform and sheafy, while a cofinal sequence of rational neighborhoods at a fixed point acquires new degree-one invariant sections that do not descend by completed rational localization. Consequently, finite quotient stability for affinoid perfectoid spaces does not extend to sousperfectoid spaces.
Comments12 pages. Revised the introduction to clarify the historical context and the relation to Hansen's 2016 quotient question and Theorem 1.2; results and proofs unchanged
