Lubin's conjecture for full $p$-adic dynamical systems
Number Theory
2016-10-14 v3
Abstract
We give a short proof of a conjecture of Lubin concerning certain families of -adic power series that commute under composition. We prove that if the family is full (large enough), there exists a Lubin-Tate formal group such that all the power series in the family are endomorphisms of this group. The proof uses ramification theory and some -adic Hodge theory.
Cite
@article{arxiv.1603.03631,
title = {Lubin's conjecture for full $p$-adic dynamical systems},
author = {Laurent Berger},
journal= {arXiv preprint arXiv:1603.03631},
year = {2016}
}
Comments
7 pages. v3: final version, to appear in the Pub Math Besan\c{c}on