Vol. 9, No. 8, 2015

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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

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.

p-adic Hodge theory, ramification theory
Mathematical Subject Classification 2010
Primary: 11S15
Received: 27 February 2015
Revised: 28 May 2015
Accepted: 25 June 2015
Published: 29 October 2015
Shun Ohkubo
Graduate School of Mathematics
Nagoya University
Nagoya 4648602