Vol. 6, No. 8, 2012

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On the refined ramification filtrations in the equal characteristic case

Liang Xiao

Vol. 6 (2012), No. 8, 1579–1667
Abstract

Let k be a complete discrete valuation field of equal characteristic p > 0. Using the tools of p-adic differential modules, we define refined Artin and Swan conductors for a representation of the absolute Galois group Gk with finite local monodromy; this leads to a description of the subquotients of the ramification filtration on Gk. We prove that our definition of the refined Swan conductors coincides with that given by Saito, which uses étale cohomology. We also study its relation with the toroidal variation of Swan conductors.

Keywords
ramification filtration, Swan conductor, refined Swan conductor, p-adic differential module, Dwork isocrystal
Mathematical Subject Classification 2000
Primary: 11S15
Secondary: 14G22, 11S80, 11S31
Milestones
Received: 10 June 2010
Revised: 19 December 2011
Accepted: 17 January 2012
Published: 14 December 2012
Authors
Liang Xiao
Department of Mathematics
University of Chicago
5734 S. University Ave
Chicago, IL 60637
United States