Multidimensional theorem of shafarevich and serre

Let H be the group obtained by taking the product of n copies of the maximal ideal of the ring of integers 0 of a local field of characteristic 0 with an algebraically closed residue field k of characteristic p>0, and let the composition law be defined as for an n-parametric commutative formal group over 0. Let the kernel of multiplication by p in H be finite. A filtration p^mH (m0 is an integer) in H is introduced whose properties allow us to obtain an exact sequence of proalgebraic groups 0Z _p ^r W^sH 0, where Z_p and W are the additive groups of p-adic integers and Witt vectors of infinite length over k, respectively; r0 and s>0 are integers.Translated from Matematicheskie Zametki, Vol. 13, No. 4, pp. 573–576, April, 1973.In conclusion, I would like to thank O. N. Vvedenskii, under whose guidance this paper was completed.