On ramification filtrations and p-adic differential modules, I: the equal characteristic case

Xiao, Liang

doi:10.2140/ant.2010.4.969

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

On ramification filtrations and $p$-adic differential modules, I: the equal characteristic case

Liang Xiao

Vol. 4 (2010), No. 8, 969–1027

DOI: 10.2140/ant.2010.4.969

Abstract

Let $k$ be a complete discretely valued field of equal characteristic $p > 0$ with possibly imperfect residue field, and let $G_{k}$ be its Galois group. We prove that the conductors computed by the arithmetic ramification filtrations on $G_{k}$ defined by Abbes and Saito (Amer. J. Math 124:5, 879–920) coincide with the differential Artin conductors and Swan conductors of Galois representations of $G_{k}$ defined by Kedlaya (Algebra Number Theory 1:3, 269–300). As a consequence, we obtain a Hasse–Arf theorem for arithmetic ramification filtrations in this case. As applications, we obtain a Hasse–Arf theorem for finite flat group schemes; we also give a comparison theorem between the differential Artin conductors and Borger’s conductors (Math. Ann. 329:1, 1–30).

Keywords

ramification, $p$-adic differential equation, Swan conductors, Artin conductors, Hasse–Arf theorem

Mathematical Subject Classification 2000

Primary: 11S15

Secondary: 14G22, 12H25

Milestones

Received: 14 May 2009

Revised: 25 May 2010

Accepted: 22 June 2010

Published: 24 February 2011

Authors

Liang Xiao
University of Chicago 321 Eckhart Hall 5734 S University Avenue Chicago, IL 60637 United States

Vol. 4, No. 8, 2010