Time: Dec 12, 13, 18, 19, 25, 26, Jan 2, 2:00-4:00pm; Jan 3, 10-12am

Abstract: Algebraic K-theory is an important invariant of rings, which is related to number theory, algebraic geometry, and topology. Unfortunately, it is very hard to compute even for rings as simple as Z/n. Recently the development of p-adic geometry has provided powerful tools for its computation. For example, Antieau, Krause, and Nikolaus claimed that they have an algorithm to compute higher K-theory of Z/n with prismatic cohomology and they have found some patterns in these higher K-groups. This short course aims to cover basic knowledge of algebraic K-theory and prismatic cohomology, as well as their interactions. The course’s content is subject to change according to the progress and audience.

摘要：代数K理论是环的重要不变量，与数论、代数几何、拓扑都有一定联系，然而它计算起来非常困难，甚至对于简单的有限环如Z/n我们都知之甚少。近些年p进几何的发展给其计算提供了有力工具，比如Antieau、Krause、Nikolaus就声称用棱镜上同调能得到计算Z/n的高阶K理论的算法，还找出了一些规律。本短期课将讲述代数K理论和棱镜上同调的基础知识，并介绍它们的联系。课程内容可能随进度以及听众意愿而调整。