Lubin's conjecture for full $p$-adic dynamical systems

Laurent Berger

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arXiv · 1603.03631

Lubin's conjecture for full $p$-adic dynamical systems

Laurent Berger

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Abstract

We give a short proof of a conjecture of Lubin concerning certain families of $p$-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 $p$-adic Hodge theory.

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Laurent Berger. 2016-10-13. Lubin's conjecture for full $p$-adic dynamical systems. https://arxiv.org/abs/1603.03631

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