TR with logarithmic poles and the de Rham-Witt complex
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915042559000576 |
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| author | Andriopoulos, Faidon |
| author_facet | Andriopoulos, Faidon |
| contents | In the article of Hesselholt [Hes05], a set of conjectures is laid out. Given a smooth scheme $X$ over the ring of integers $\mathcal{O}_K$ of a $p$-adic field $K$, these conjectures concern the expected relation between log topological restriction homology $\mathrm{TR}^r (X,M_X)$ and the absolute log de Rham--Witt complex $W_rΩ_{(X,M_X)}$.
In this note, which is companion to [And24a], we discuss the case of a $p$-completely smooth $p$-adic formal scheme $X$ over $\mathrm{spf} \mathcal{O}_C$, where $C$ is the field of $p$-adic complex numbers.
Along the way, we study the motivic filtration of log $\mathrm{TR}^r$ and its $S^1$-homotopy fixed points, following ideas of [Bin+23]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | TR with logarithmic poles and the de Rham-Witt complex Andriopoulos, Faidon Algebraic Geometry K-Theory and Homology In the article of Hesselholt [Hes05], a set of conjectures is laid out. Given a smooth scheme $X$ over the ring of integers $\mathcal{O}_K$ of a $p$-adic field $K$, these conjectures concern the expected relation between log topological restriction homology $\mathrm{TR}^r (X,M_X)$ and the absolute log de Rham--Witt complex $W_rΩ_{(X,M_X)}$. In this note, which is companion to [And24a], we discuss the case of a $p$-completely smooth $p$-adic formal scheme $X$ over $\mathrm{spf} \mathcal{O}_C$, where $C$ is the field of $p$-adic complex numbers. Along the way, we study the motivic filtration of log $\mathrm{TR}^r$ and its $S^1$-homotopy fixed points, following ideas of [Bin+23]. |
| title | TR with logarithmic poles and the de Rham-Witt complex |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2412.00929 |