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arXiv · 2412.00929

TR with logarithmic poles and the de Rham-Witt complex

Faidon Andriopoulos
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Abstract

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 $W_r\Omega_{(X,M_X)}$. 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].

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Faidon Andriopoulos. 2024-12-01. TR with logarithmic poles and the de Rham-Witt complex. https://arxiv.org/abs/2412.00929

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