On the $p$-adic deformation problem for the $K$-theory of semistable schemes
Algebraic Geometry
2026-05-25 v2
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 -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 -adic Lefschetz -theorem.
Keywords
Cite
@article{arxiv.2601.14146,
title = {On the $p$-adic deformation problem for the $K$-theory of semistable schemes},
author = {Federico Binda and Tommy Lundemo and Alberto Merici and Doosung Park},
journal= {arXiv preprint arXiv:2601.14146},
year = {2026}
}
Comments
23 pages. Corrected a gap in the proof of Prop. 2.12. References updated