论文标题
完成的棱柱形$ f $ -crystals and Crystalline $ \ Mathbf {z} _p $ -local Systems
Completed prismatic $F$-crystals and crystalline $\mathbf{Z}_p$-local systems
论文作者
论文摘要
我们介绍了在平滑$ p $ adiC正式计划的绝对棱镜网站上完成的$ f $ -crystals的概念。我们从已完成的Prismatic $ f $ -crystals的类别定义一个函子，以晶体的étale$ \ mathbf {z} _p $ - 局部系统的通用纤维上的正式方案中的函数，并表明它给出了类别等效的类别。这概括了Bhatt和Scholze的工作，该工作将完美的残留物领域的完整离散估值环处理。
We introduce the notion of completed $F$-crystals on the absolute prismatic site of a smooth $p$-adic formal scheme. We define a functor from the category of completed prismatic $F$-crystals to that of crystalline étale $\mathbf{Z}_p$-local systems on the generic fiber of the formal scheme and show that it gives an equivalence of categories. This generalizes the work of Bhatt and Scholze, which treats the case of a complete discrete valuation ring with perfect residue field.
