Topological cyclic homology for p-adic local fields

Topological cyclic homology, which was introduced by Bokstedt-Hsiang-Madsen in 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.