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

Ohkubo, Shun

doi:10.2140/ant.2015.9.1881

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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 $(0, p)$ 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 $ℕ_{dR}$ that associates a de Rham representation $V$ to a $(φ, \nabla)$ -module in the sense of Kedlaya. Finally, we prove a compatibility between Kedlaya’s differential Swan conductor of $ℕ_{dR} (V)$ and the Swan conductor of $V$ , which generalizes Marmora’s formula.

Keywords

p-adic Hodge theory, ramification theory

Mathematical Subject Classification 2010

Primary: 11S15

Milestones

Received: 27 February 2015

Revised: 28 May 2015

Accepted: 25 June 2015

Published: 29 October 2015

Authors

Shun Ohkubo
Graduate School of Mathematics Nagoya University Furocho Chikusaku Nagoya 4648602 Japan

Vol. 9, No. 8, 2015