On the ramification theory of two-dimensional local fields

Filtrations are defined on the group $K_2^\operatorname{top}$ of a two-dimensional local field of characteristic $p>0$ and on the Galois group of its $p$-extension. Results are proved which are analogous to the one-dimensional case (Proposition 2.4, Theorem 2.1).
It is proved that, for an Artin–Schreier extension $L/K$ the reciprocity map carries the filtration on the group $ K_2^{\operatorname{top}}(K)$ to the filtration on the group $ \operatorname{Gal}(L/K)$, with the Herbrand numbering. An example is given which shows that this is not true for an arbitrary $p$-extension.
Bibliography: 7 titles.