Mathematical Research Letters

Volume 20 (2013)

Number 3

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

Pages: 409 – 428

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n3.a1

Author

Laurent Berger (UMPA, École Normal Supérieure de Lyon, France)

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 $(\varphi, \Gamma)$-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 $\varphi$-module using a modification process. We prove that we obtain every crystalline $(\varphi, \Gamma)$-module over those rings in this way.

Keywords

$(\varphi, \Gamma)$-module, Lubin-Tate group, filtered $\varphi$-module, crystalline representation, $p$-adic period, Fontaine theory, reflexive sheaf

2010 Mathematics Subject Classification

11Fxx, 11Sxx, 14Gxx

Full Text (PDF format)