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1 December 2022 On the Beilinson fiber square
Benjamin Antieau, Akhil Mathew, Matthew Morrow, Thomas Nikolaus
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Duke Math. J. 171(18): 3707-3806 (1 December 2022). DOI: 10.1215/00127094-2022-0037

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. "On the Beilinson fiber square." Duke Math. J. 171 (18) 3707 - 3806, 1 December 2022. https://doi.org/10.1215/00127094-2022-0037

Information

Received: 25 January 2021; Revised: 29 September 2021; Published: 1 December 2022
First available in Project Euclid: 10 November 2022

Digital Object Identifier: 10.1215/00127094-2022-0037

Subjects:
Primary: 14F30
Secondary: 14F40 , 19D55 , 19E15

Keywords: Cyclic homology , deformation of algebraic cycles , motivic cohomology , p-adic K-theory

Rights: Copyright © 2022 Duke University Press

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Vol.171 • No. 18 • 1 December 2022
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