I am curious to find an example of a 1-d formal group law that does not come from a splitting of the formal group law of an abelian variety.
I am aware that we can craft logarithms from the formal Brauer group, but can formal group laws obtained in this way also be thought of as coming from integrating an invariant differential of an abelian variety?
Do formal group laws that come from formal Brauer groups of a variety lose the ability to be studied via the p-divisible group of the Jacobian of that variety?