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      Multivariable Lubin-Tate (\phi,\Gamma)-modules and filtered \phi-modules

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          Abstract

          We define some rings of power series in several variables, that are attached to a Lubin-Tate formal module. We then give some examples of (\phi,\Gamma)-modules over those rings. They are the global sections of some reflexive sheaves on the p-adic open unit polydisk, that are constructed from a filtered \phi-module using a modification process. We prove that we obtain every crystalline (\phi,\Gamma)-module over those rings in this way.

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          Non-Archimedean Analysis

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            Author and article information

            Journal
            2012-11-19
            2013-04-19
            Article
            1211.4431
            21137813-9bf5-4dd7-9a7d-06db2a2d359e

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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            11F, 11S, 14G
            This version corrects a mistake from v1: the module M^+(D) is reflexive, but I do not know whether or not it is projective in general. The main theorems and various definitions have been amended as a result. Some other less significant mistakes have been corrected as well. 22 pages
            math.NT math.RT

            Number theory,Algebra
            Number theory, Algebra

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