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2007 Swan conductors for p-adic differential modules, I: A local construction
Kiran Kedlaya
Algebra Number Theory 1(3): 269-300 (2007). DOI: 10.2140/ant.2007.1.269

Abstract

We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect. We also establish analogues of some key properties of the usual Swan conductor, such as integrality (the Hasse–Arf theorem), and the fact that the graded pieces of the associated ramification filtration on Galois groups are abelian and killed by p.

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Kiran Kedlaya. "Swan conductors for p-adic differential modules, I: A local construction." Algebra Number Theory 1 (3) 269 - 300, 2007. https://doi.org/10.2140/ant.2007.1.269

Information

Received: 12 February 2007; Revised: 13 August 2007; Accepted: 17 September 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1184.11051
MathSciNet: MR2361935
Digital Object Identifier: 10.2140/ant.2007.1.269

Subjects:
Primary: 11S15
Secondary: 14F30

Rights: Copyright © 2007 Mathematical Sciences Publishers

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