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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.12136 |
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Table of Contents:
- Let $k$ be a perfect field of characteristic $p > 0$. For a strictly semi-stable scheme over $k[[t]]$, we construct the weight spectral sequence in $p$-adic cohomology using the theory of arithmetic $\mathcal{D}$-modules, whose $E_1$ terms are described by rigid cohomologies of irreducible components of the closed fiber and whose $E_\infty$ terms are conjecturally described by the (unipotent) nearby cycle of Lazda-Pál's rigid cohomology over the bounded Robba ring. We also show its functoriality by pushforward and state the conjecture of its functoriality by pullback and dual.