Topological K-groups of two-dimensional local fields
A complete two-dimensional local field K of mixed characteristic with finite second residue field is considered. The existence of a completely ramified extension L of K such that L is a standard field is assumed. It is proved that the rank of the quotient U(1)K 2 top K/TK, where TK is the closure of the torsion subgroup, is equal to the degree of the constant subfield of K over ℚp. I. B. Zhukov constructed a set of generators of this quotient in the case where K is a standard field. In this paper, two natural generalizations of this set are considered, and it is proved that one of them generates the entire group and the other generates its subgroup of finite index. Bibliography: 5 titles.
KeywordsLocal Parameter Galois Extension Mixed Characteristic Torsion Subgroup Standard Field
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- 3.I. B. Zhukov and A. I. Madunz, “Additive and multiplicative decompositions in higher-dimensional local fields,” Zap. Nauchn. Semin. POMI, 272, 186–196 (2000).Google Scholar