Abstract:We establish a semistable generalization of the Beilinson-Bloch-Esnault-Kerz fiber square, relating the algebraic K-theory of a semistable scheme to its logarithmic topological cyclic homology. We prove that the obstruction to lifting K-theory classes is governed by the Hyodo-Kato Chern character. This answers the $p$-adic deformation problem for continuous K-theory in the semistable case, extending the work of Antieau-Mathew-Morrow-Nikolaus. As an application, we provide a purely K-theoretic proof of Yamashita's semistable $p$-adic Lefschetz $(1,1)$-theorem.
| Comments: | 23 pages. Corrected a gap in the proof of Prop. 2.12. References updated |
| Subjects: | Algebraic Geometry (math.AG) |
| Cite as: | arXiv:2601.14146 [math.AG] |
| (or arXiv:2601.14146v2 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2601.14146 arXiv-issued DOI via DataCite |
From: Federico Binda [view email]
[v1]
Tue, 20 Jan 2026 16:50:39 UTC (28 KB)
[v2]
Fri, 22 May 2026 07:25:59 UTC (29 KB)
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