For each $n > 0$ there is a unique 1-dimensional commutative formal group law $F$ over $\mathbf{Z}$, $F(X, Y) = X + Y + \dots \in \mathbf{Z}[[X, Y]]$, whose logarithm function is given by $$l(x) = \sum_{k \ge 0} \frac{x^{p^{nk}}}{p^k}.$$

For $p$ prime, let $\bar{F} \in \mathbf{F}_p[[X, Y]]$ be the formal group over $\mathbf{F}_p$ given by reduction of $F$ modulo $p$. (Cf. Prop. 9.25 in http://neil-strickland.staff.shef.ac.uk/courses/formalgroups/fg.pdf.)

Is $\bar{F}$ an element of $\mathbf{F}_p[X] [[Y]]$?

Thank you for your answers.

Let $p$ be a prime. For each $n > 0$ there is a unique 1-dimensional commutative formal group law $F$ over $\mathbf{Z}$, $F(X, Y) = X + Y + \dots \in \mathbf{Z}[[X, Y]]$, whose logarithm function is given by $$l(x) = \sum_{k \ge 0} \frac{x^{p^{nk}}}{p^k}.$$

Let $\bar{F} \in \mathbf{F}_p[[X, Y]]$ be the formal group over $\mathbf{F}_p$ given by reduction of $F$ modulo $p$. (Cf. Prop. 9.25 in http://neil-strickland.staff.shef.ac.uk/courses/formalgroups/fg.pdf.)

Is $\bar{F}$ an element of $\mathbf{F}_p[X] [[Y]]$?

Thank you for your answers.

Is the formal group law $\bar{F}$ from Prop. 9.25 in http://neil-strickland.staff.shef.ac.uk/courses/formalgroups/fg.pdf

an element of $\mathbb{F_p}[X] [[Y]]$?

Thank you for your answers.

For each $n > 0$ there is a unique 1-dimensional commutative formal group law $F$ over $\mathbf{Z}$, $F(X, Y) = X + Y + \dots \in \mathbf{Z}[[X, Y]]$, whose logarithm function is given by $$l(x) = \sum_{k \ge 0} \frac{x^{p^{nk}}}{p^k}.$$

For $p$ prime, let $\bar{F} \in \mathbf{F}_p[[X, Y]]$ be the formal group over $\mathbf{F}_p$ given by reduction of $F$ modulo $p$. (Cf. Prop. 9.25 in http://neil-strickland.staff.shef.ac.uk/courses/formalgroups/fg.pdf.)

Is $\bar{F}$ an element of $\mathbf{F}_p[X] [[Y]]$?

Thank you for your answers.