#### 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
##### Abstract

We construct noncommutative multidimensional versions of overconvergent power series rings and Robba rings. We show that the category of étale $\left(\phi ,\Gamma \right)$-modules over certain completions of these rings is equivalent to the category of étale $\left(\phi ,\Gamma \right)$-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