Vol. 8, No. 1, 2014

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

Gergely Zábrádi

Vol. 8 (2014), No. 1, 191–242

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 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.

overconvergent, Robba ring, noncommutative, $(\varphi,\Gamma)$-module
Mathematical Subject Classification 2010
Primary: 11F70
Secondary: 20G25, 16U20
Received: 18 August 2012
Revised: 5 April 2013
Accepted: 7 May 2013
Published: 20 April 2014
Gergely Zábrádi
Department of Algebra and Number Theory
Institute of Mathematics
Eötvös Loránd University
Pázmány Péter sétány 1/C
Budapest H-1117