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

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 vector bundles 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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Contributor : Laurent Berger <>
Submitted on : Tuesday, November 20, 2012 - 10:14:21 AM
Last modification on : Thursday, April 4, 2019 - 10:18:04 AM

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  • HAL Id : hal-00754931, version 1
  • ARXIV : 1211.4431



Laurent Berger. Multivariable Lubin-Tate (\phi,\Gamma)-modules and filtered \phi-modules. Mathematical Research Letters, 2013, 20 (3), pp.409--428. 〈hal-00754931〉



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