Abstract

Topological cyclic homology, which was introduced by Bökstedt–Hsiang–Madsen in the early 90s, is an important tool to compute algebraic K-groups via the cyclotomic trace map.  It is also closely related to p-adic cohomology theories as revealed by the recent work of Bhatt–Morrow–Scholze.  In this talk, we will give a brief introduction to topological cyclic homology and present a new approach to computing it in the case of p-adic local fields.  Joint work with Guozhen Wang.

About the speaker

Ruochuan Liu is a Boya Distinguished Professor in mathematics of Peking University.  His current research focuses on p-adic aspects of arithmetic geometry and number theory, especially p-adic Hodge theory, p-adic automophic forms and p-adic Langlands program.  In 2017, he received the National Science Fund for Distinguished Young Scholars.  He was awarded the Tencent Xplorer prize in 2019, and the China Youth Science and Technology Award in 2020.