On the refined ramification filtrations in the equal characteristic case

Xiao, Liang

doi:10.2140/ant.2012.6.1579

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On the refined ramification filtrations in the equal characteristic case

Liang Xiao

Vol. 6 (2012), No. 8, 1579–1667

DOI: 10.2140/ant.2012.6.1579

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 $G_{k}$ with finite local monodromy; this leads to a description of the subquotients of the ramification filtration on $G_{k}$ . 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

Vol. 6, No. 8, 2012