论文标题
通过附近的循环上的一般基座，代数可刚性分析品种的典型刚性刚性分析品种的典范
Étale cohomology of algebraizable rigid analytic varieties via nearby cycles over general bases
论文作者
论文摘要
我们证明了有限的定理，并且是刚性分析品种的典型理论中的比较定理。由于Huber的结果，对于准连接的刚性分析品种的分离形态，目标是尺寸为$ \ le1 $，紧凑的高直接图像可保留准构造性。尽管对具有较高维度靶标的形态的类似陈述通常失败了，但我们证明，在代数的情况下，它在用修改替换目标后成立。我们从已知的有限性中推断出它在一般基础上附近周期的理论中得出的结果，并获得了新的比较结果，从而鉴定了紧凑型高的直接图像束系，直到对目标进行修改，以附近的周期在一般基础上。
We prove a finiteness theorem and a comparison theorem in the theory of étale cohomology of rigid analytic varieties. By a result of Huber, for a quasi-compact separated morphism of rigid analytic varieties with target being of dimension $\le1$, the compactly supported higher direct image preserves quasi-constructibility. Though the analogous statement for morphisms with higher dimensional target fails in general, we prove that, in the algebraizable case, it holds after replacing the target with a modification. We deduce it from a known finiteness result in the theory of nearby cycles over general bases and a new comparison result, which gives an identification of the compactly supported higher direct image sheaves, up to modification of the target, in terms of nearby cycles over general bases.
