On the Beilinson fiber square

Antieau, Benjamin; Mathew, Akhil; Morrow, Matthew; Nikolaus, Thomas

Abstract

Using topological cyclic homology, we give a refinement of Beilinson's p-adic Goodwillie isomorphism between relative continuous K-theory and cyclic homology. As a result, we generalize results of Bloch-Esnault-Kerz and Beilinson on the p-adic deformations of K-theory classes. Furthermore, we prove structural results for the Bhatt-Morrow-Scholze filtration on TC and identify the graded pieces with the syntomic cohomology of Fontaine-Messing.