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

We construct noncommutative multidimensional versions of overconvergent power series rings and Robba rings. We show that the category of étale \((\varphi,\Gamma)\)-modules over certain completions of these rings are equivalent to the category of étale \((\varphi,\Gamma)\)-modules over the correspond...

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Bibliographic Details
Published in:arXiv.org 2013-04
Main Author: Zábrádi, Gergely
Format: Article
Language:English
Subjects:
Modules
Object recognition
Power series
Online Access:Get full text
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Summary:We construct noncommutative multidimensional versions of overconvergent power series rings and Robba rings. We show that the category of étale \((\varphi,\Gamma)\)-modules over certain completions of these rings are equivalent to the category of étale \((\varphi,\Gamma)\)-modules over the corresponding classical overconvergent, resp. Robba rings (hence also to the category of \(p\)-adic Galois representations of \(\mathbb{Q}_p\)). Moreover, in the case of Robba rings, the assumption of étaleness is not necessary, so there exists a notion of trianguline objects in this sense.
ISSN:2331-8422
DOI:10.48550/arxiv.1208.3347