The aim of this paper is to answer a question of Coates and Greenberg: let F be a commutative m-dimensional formal group over the ring of integers of a local field k, and let K be an algebraic extension of k with infinite ramification index. Denote by M_R the maximal ideal in the ring of integers of the separable closure of K. Suppose that the height of F is greater than m. Does H¹(K, F(_K^m)) = 0 imply that K is deeply ramified? The answer is positive.