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Consider the case of a formal group $G$ of finite height over a complete local Noetherian ring $R$ of residue characteristic $p>0$. For each $m$ there is a finite $R$-algebra $S$ that classifies fini …

Let $D$ be the divided power ring $$ D = \mathbb{Z}[a_0,a_1,a_2,\dotsc]/(a_0-1,a_na_m-(n,m)a_{n+m}) $$ (where $(n,m)$ denotes the binomial coefficient $(n+m)!/(n!\,m!)$). Then ring maps from $D$ to …

For endomorphisms of $F_m$ one should consider the ring of numerical polynomials: $$ P = \{f(a)\in \mathbb{Q}[a]: f(\mathbb{Z})\subseteq\mathbb{Z}\} $$ The functions $b_i(a)=\left(\begin{array}{c}a\\ …

This is really a comment, but a bit too long. The coefficient of $y$ in $F(x,y)$ is $1/l'(x)$. If $n=1$ then $l'(x)=\sum_ix^{p^i-1}$ and $1/l'(x)$ is not polynomial mod $p$, so the answer is negativ …

No, at least when $p=2$ the coefficient of $x^8$ in the relevant power series is not 2-locally integral. I have put a Maple worksheet at https://strickland1.org/misc/ArHaz.mw with a PDF version at ht …

I'll refer to my notes on formal groups at https://strickland1.org/courses/formalgroups/fg.pdf. There are results about the formal group law of an elliptic curve in Section 19. That is written in te …

One-dimensional algebraic groups are essentially multiplicative, elliptic curves, or additive, so their associated formal groups have height $1$, $2$ or $\infty$. There exist one-dimensional commutat …

I'll assume that $\pi=p$; I guess that the general case is the same but I have not checked. We now have $k=\mathbb{F}_{p^n}$ and $\mathcal{O}_K=W\mathbb{F}_{p^n}$. The group of roots of unity in $W\ …

This is really just a comment. Your question is equivalent to the following: if we have a formal group law $$ F(x,y) = x + y + \sum_{i,j>0} a_{ij}x^iy^j \in \mathbb{Q}[[x,y]] $$ with $a_{1j}\geq 0$ f …