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arXiv · 2606.25726

Integrality of height-one formal groups

Martin Debaisieux
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Abstract

Let $K$ be a finite extension of $\mathbb{Q}_p$. We prove that a one-dimensional formal group law over $K$ has integral coefficients if and only if its multiplication-by-$n$ endomorphisms have integral coefficients for all integers $n$, in the height-one case, i.e. when the multiplication by $p$ has Weierstrass degree $p$. The proof uses some $p$-adic Hodge theory.

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Martin Debaisieux. 2026-06-24. Integrality of height-one formal groups. https://arxiv.org/abs/2606.25726

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