论文标题
钻石上的本地系统和$ p $ - adic矢量捆绑包
Local systems on diamonds and $p$-adic vector bundles
论文作者
论文摘要
我们使用Scholze的钻石框架来获得$ P $ - adiC矢量束和本地系统之间的对应关系的新见解。在消失的希格斯字段的情况下，这种通信是在$ p $ - 亚种辛普森理论的背景下产生的。在本文中，我们提供了针对典型，Pro-étale和$ v $ - 学术的钻石上本地系统的详细分析，并研究有关所有三种拓扑的结构束线条。应用于$ \ mathbb {c} _p $的有限类型的适当的ADIC空间，这使我们能够证明$ \ Mathbb {C} _p $ local-local systems具有积分模型的类别等效性，而模块下的模块则在每个$ p^neaf中都可以覆盖，以适用于$ p^n $ coverial coverial coppy of poss comport corpecor。 $ V $ - 学术的灵活性以及在本地系统的积分模型上的下降结果使我们可以证明，可以在任何正常的适当盖上检查模块类别中的琐事性条件。该结果导致了Deninger的平行传输理论的扩展，第二作者在适当的正常覆盖层上以数值平坦的降低为载体束。
We use Scholze's framework of diamonds to gain new insights in correspondences between $p$-adic vector bundles and local systems. Such correspondences arise in the context of $p$-adic Simpson theory in the case of vanishing Higgs fields. In the present paper we provide a detailed analysis of local systems on diamonds for the étale, pro-étale, and the $v$-topology, and study the structure sheaves for all three topologies in question. Applied to proper adic spaces of finite type over $\mathbb{C}_p$ this enables us to prove a category equivalence between $\mathbb{C}_p$-local systems with integral models, and modules under the $v$-structure sheaf which modulo each $p^n$ can be trivialized on a proper cover. The flexibility of the $v$-topology together with a descent result on integral models of local systems allows us to prove that the trivializability condition in the module category may be checked on any normal proper cover. This result leads to an extension of the parallel transport theory by Deninger and the second author to vector bundles with numerically flat reduction on a proper normal cover.
