论文标题
Perfectoid Towers及其倾斜：应用于当地对数戒指的典型同居组
Perfectoid towers and their tilts : with an application to the étale cohomology groups of local log-regular rings
论文作者
论文摘要
为了启动有关完美素方法在Noetherian戒指的应用的系统研究，我们介绍了PerfectOdoid Towers及其倾斜的概念。我们主要表明倾斜操作保留了几种同源不变和有限性能。使用此功能，我们还为倾斜下的欧特尔共同体学组提供了比较结果。作为一个应用程序，我们证明了在混合特征情况下，在对数几何形状中出现的局部对数定型环的Divisor类组的Prime-to-P $ Torsion子组的有限性。
To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the tilting operation preserves several homological invariants and finiteness properties. Using this, we also provide a comparison result on étale cohomology groups under the tilting. As an application, we prove finiteness of the prime-to-$p$-torsion subgroup of the divisor class group of a local log-regular ring that appears in logarithmic geometry in the mixed characteristic case.
