\(K\)-groups of multidimensional local fields (Q920150)

It is given a full description of the structure of the group \(K_ 2^{top}(F)\) in the case where \(F\) is a two dimensional local field of mixed characteristics. The proof uses an explicit expression for the Hilbert symbol in the two dimensional case obtained by \textit{S. V. Vostokov} [Izv. Akad. Nauk SSSR, Ser. Mat. 49, No. 2, 283--308 (1985; Zbl 0608.12017)]. As a corollary the author proves that the kernel of the canonical map \(K^ M_ 2(F)\to K_ 2^{top}(F)\) coincides with the infinitely divisible elements in Milnor's group \(K^ M_ 2(F)\).