Multivariable Lubin-Tate (\phi,\Gamma)-modules and filtered \phi-modules
Number Theory
2013-04-22 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.1211.4431,
title = {Multivariable Lubin-Tate (\phi,\Gamma)-modules and filtered \phi-modules},
author = {Laurent Berger},
journal= {arXiv preprint arXiv:1211.4431},
year = {2013}
}
Comments
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