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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.14146 |
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| _version_ | 1866918517186494464 |
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| author | Binda, Federico Lundemo, Tommy Merici, Alberto Park, Doosung |
| author_facet | Binda, Federico Lundemo, Tommy Merici, Alberto Park, Doosung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14146 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the $p$-adic deformation problem for the $K$-theory of semistable schemes Binda, Federico Lundemo, Tommy Merici, Alberto Park, Doosung Algebraic Geometry 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. |
| title | On the $p$-adic deformation problem for the $K$-theory of semistable schemes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.14146 |