论文标题
在u^{\ infty} - 棱镜共同体中
On the u^{\infty}-torsion submodule of prismatic cohomology
论文作者
论文摘要
我们研究了在整数padic环上平稳的正式方案的Breuil-kisin Prismatic共同体的最大有限长度子模块。该基部控制整体P-ADIC共同体理论中的病理现象。几何应用包括（1）特征p中两个天然相关的阿尔巴尼斯品种之间的差异，以及（2）P-Adicétale共同体中专业图的内核。作为算术应用，我们研究了由于Fontaine-Laffaille，Fontaine-Messing和Kato引起的理论边界案例。还包括一个有趣的例子，它是根据Bhatt-Morrow-Scholze的作品中的建设中概括的，（1）说明了我们的一些理论结果是敏锐的，并且（2）否定了Breuil的问题。
We investigate the maximal finite length submodule of the Breuil-Kisin prismatic cohomology of a smooth proper formal scheme over a p-adic ring of integers. This submodule governs pathology phenomena in integral p-adic cohomology theories. Geometric applications include a control, in low degrees and mild ramifications, of (1) the discrepancy between two naturally associated Albanese varieties in characteristic p, and (2) kernel of the specialization map in p-adic étale cohomology. As an arithmetic application, we study the boundary case of the theory due to Fontaine-Laffaille, Fontaine-Messing, and Kato. Also included is an interesting example, generalized from a construction in Bhatt-Morrow-Scholze's work, which (1) illustrates some of our theoretical results being sharp, and (2) negates a question of Breuil.
