Algebra & Number Theory
- Algebra Number Theory
- Volume 9, Number 8 (2015), 1881-1954.
On differential modules associated to de Rham representations in the imperfect residue field case
Let be a complete discrete valuation field of mixed characteristic with possibly imperfect residue fields, and let the absolute Galois group of . In the first part of this paper, we prove that Scholl’s generalization of fields of norms over is compatible with Abbes–Saito’s ramification theory. In the second part, we construct a functor that associates a de Rham representation to a -module in the sense of Kedlaya. Finally, we prove a compatibility between Kedlaya’s differential Swan conductor of and the Swan conductor of , which generalizes Marmora’s formula.
Algebra Number Theory, Volume 9, Number 8 (2015), 1881-1954.
Received: 27 February 2015
Revised: 28 May 2015
Accepted: 25 June 2015
First available in Project Euclid: 16 November 2017
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Primary: 11S15: Ramification and extension theory
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