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arXiv · 2003.12541

On the Beilinson fiber square

Benjamin Antieau·Akhil Mathew·Matthew Morrow·Thomas Nikolaus
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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.

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Benjamin Antieau, Akhil Mathew, Matthew Morrow, Thomas Nikolaus. 2020-03-27. On the Beilinson fiber square. https://arxiv.org/abs/2003.12541

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