#### Vol. 9, No. 8, 2015

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editors' Interests Submission Guidelines Submission Form Editorial Login Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
On differential modules associated to de Rham representations in the imperfect residue field case

### Shun Ohkubo

Vol. 9 (2015), No. 8, 1881–1954
DOI: 10.2140/ant.2015.9.1881
##### Abstract

Let $K$ be a complete discrete valuation field of mixed characteristic $\left(0,p\right)$ with possibly imperfect residue fields, and let ${G}_{K}$ 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 that associates a de Rham representation $V$ to a $\left(\phi ,\nabla \right)$-module in the sense of Kedlaya. Finally, we prove a compatibility between Kedlaya’s differential Swan conductor of and the Swan conductor of $V$, which generalizes Marmora’s formula.