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IF 2.3 1区数学 Q1 MATHEMATICS

Duke Mathematical Journal Pub Date : 2020-03-27 DOI:10.1215/00127094-2022-0037

Benjamin Antieau, A. Mathew, M. Morrow, T. Nikolaus

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引用次数: 21

摘要

利用拓扑循环同构，给出了相对连续$K$-理论与循环同构之间的Beilinson $p$-adic Goodwillie同构的一个改进。因此，我们推广了Bloch-Esnault-Kerz和Beilinson关于K -理论类的p -adic变形的结果。进一步，我们证明了$TC$上的bhat - morrow - scholze滤波的结构结果，并利用Fontaine-Messing的对子上同调对分级块进行了识别。

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On the Beilinson fiber square

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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