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 pmH (m≥0 is an integer) in H is introduced whose properties allow us to obtain an exact sequence of proalgebraic groups 0→Z p r →Ws→H→ 0, where Zp and W are the additive groups of p-adic integers and Witt vectors of infinite length over k, respectively; r≥0 and s>0 are integers.
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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.
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Konovalov, G.T. Multidimensional theorem of shafarevich and serre. Mathematical Notes of the Academy of Sciences of the USSR 13, 346–348 (1973). https://doi.org/10.1007/BF01146572
- Exact Sequence
- Formal Group
- Local Field
- Additive Group