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arXiv · 1307.8110

On differential modules associated to de Rham representations in the imperfect residue field case

Shun Ohkubo
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Abstract

Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$, whose residue field may not be perfect, and $G_K$ the absolute Galois group of $K$. In the first part of this paper, we prove that Scholl's generalization of fields of norms over $K$ is compatible with Abbes-Saito's ramification theory. In the second part, we construct a functor $\mathbb{N}_{\mathrm{dR}}(V)$ associating a de Rham representation $V$ with a $(φ,\nabla)$-module in the sense of Kedlaya. Finally, we prove a compatibility between Kedlaya's differential Swan conductor of $\mathbb{N}_{\mathrm{dR}}(V)$ and Swan conductor of $V$, which generalizes Marmora's formula.

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Shun Ohkubo. 2015-06-10. On differential modules associated to de Rham representations in the imperfect residue field case. https://doi.org/10.2140/ant.2015.9.1881

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