(φ,Γ)-modules over noncommutative overconvergent and Robba rings

Zábrádi, Gergely

doi:10.2140/ant.2014.8.191

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

$(\varphi,\Gamma)$-modules over noncommutative overconvergent and Robba rings

Gergely Zábrádi

Vol. 8 (2014), No. 1, 191–242

DOI: 10.2140/ant.2014.8.191

Abstract

We construct noncommutative multidimensional versions of overconvergent power series rings and Robba rings. We show that the category of étale $(φ, Γ)$ -modules over certain completions of these rings is equivalent to the category of étale $(φ, Γ)$ -modules over classical overconvergent or Robba rings as the case may be (hence also to the category of $p$ -adic Galois representations of $ℚ_{p}$ ). In the case of Robba rings, the assumption of étaleness is not necessary, so there exists a notion of trianguline objects in this sense.

Keywords

overconvergent, Robba ring, noncommutative, $(\varphi,\Gamma)$-module

Mathematical Subject Classification 2010

Primary: 11F70

Secondary: 20G25, 16U20

Milestones

Received: 18 August 2012

Revised: 5 April 2013

Accepted: 7 May 2013

Published: 20 April 2014

Authors

Gergely Zábrádi
Department of Algebra and Number Theory Institute of Mathematics Eötvös Loránd University Pázmány Péter sétány 1/C Budapest H-1117 Hungary

Vol. 8, No. 1, 2014