Formal groups and congruences

We give a criterion of integrality of an one-dimensional formal group law in terms of congruences satisfied by the coefficients of the canonical invariant differential. For an integral formal group law a p-adic analytic formula for the local characteristic polynomial at p is given. We demonstrate applications of our results to formal group laws attached to L-functions, Artin--Mazur formal groups of algebraic varieties and hypergeometric formal group laws. (This is the final version submitted to a journal; new parts are added in the section on hypergeometric formal group laws.)