Algebra & Number Theory

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) with possibly imperfect residue fields, and let GK 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  dR that associates a de Rham representation V to a (φ,)-module in the sense of Kedlaya. Finally, we prove a compatibility between Kedlaya’s differential Swan conductor of  dR(V ) and the Swan conductor of V , which generalizes Marmora’s formula.

Article information

Source
Algebra Number Theory, Volume 9, Number 8 (2015), 1881-1954.

Dates
Received: 27 February 2015
Revised: 28 May 2015
Accepted: 25 June 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842408

Digital Object Identifier
doi:10.2140/ant.2015.9.1881

Mathematical Reviews number (MathSciNet)
MR3418746

Zentralblatt MATH identifier
1377.11120

Subjects
Primary: 11S15: Ramification and extension theory

Keywords
p-adic Hodge theory ramification theory

Citation

Ohkubo, Shun. On differential modules associated to de Rham representations in the imperfect residue field case. Algebra Number Theory 9 (2015), no. 8, 1881--1954. doi:10.2140/ant.2015.9.1881. https://projecteuclid.org/euclid.ant/1510842408


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