In their paper Scholze and Weinstein show that a certain diagram of perfectoid spaces is Cartesian. In this paper, we generalize their result. This generalization will be used in a forthcoming paper of ours to compute certain non-trivial $\ell$-adic etale cohomology classes appearing in the the generic fiber of Lubin-Tate and Rapoprt-Zink towers. We also study the behavior of the vector bundle functor on the fundamental curve in $p$-adic Hodge theory, defined by Fargues-Fontaine, under multilinear morphisms.

中文翻译：

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Rapoport-Zink 的笛卡尔图在 $p$-可分群的普遍覆盖上高耸

在他们的论文中，Scholze 和 Weinstein 表明完美空间的某个图是笛卡尔空间图。在本文中，我们概括了他们的结果。这种概括将在我们即将发表的论文中用于计算出现在 Lubin-Tate 和 Rapoprt-Zink 塔的通用纤维中的某些非平凡的 $\ell$-adic etale 上同调类。我们还研究了向量丛函子在由 Fargues-Fontaine 定义的 $p$-adic Hodge 理论中在多线性态射下的基本曲线上的行为。