On Drinfeld's universal special formal module

Drinfeld shows that the p-adic symmetric space Ωⁿ is the moduli space of formal modules endowed with an action of a given division algebra and certain rigidified condition. He associates to such a formal module a point in Ωⁿ. His construction is analogous to computing the period lattice of an abelian variety. In this article we consider the inverse procedure of Drinfeld's construction that associates to a rigid point in Ωⁿ the rigidified formal module. We also compute the logarithm of the resulting formal module.