Lubin's conjecture for height-one $p$-adic dynamical systems

Martin Debaisieux

Lubin's conjecture for height-one $p$-adic dynamical systems

Number Theory 2026-07-03 v1 Dynamical Systems

Authors: Martin Debaisieux

Abstract

We prove Lubin's conjecture for height-one commuting pairs of formal power series defined over the ring of integers $\mathcal{O}$ of any finite extension of $\mathbb{Q}_p$ . Using some $p$ -adic Hodge theory, we show that such a pair is a pair of endomorphisms of a formal group defined over $\mathcal{O}$ .

Cite

@article{arxiv.2607.03257,
  title  = {Lubin's conjecture for height-one $p$-adic dynamical systems},
  author = {Martin Debaisieux},
  journal= {arXiv preprint arXiv:2607.03257},
  year   = {2026}
}

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6 pages