Vol. 6, No. 8, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
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