Geodesic
On the ramification theory of two-dimensional local fields
Sbornik. Mathematics, Tome 37 (1980) no. 3, pp. 349-365 
V. G. Lomadze. On the ramification theory of two-dimensional local fields. Sbornik. Mathematics, Tome 37 (1980) no. 3, pp. 349-365. http://geodesic.mathdoc.fr/item/SM_1980_37_3_a3/
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     title = {On the ramification theory of two-dimensional local fields},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] A. N. Parshin, “Polya klassov i algebraicheskaya $K$-teoriya”, Uspekhi matem. nauk, XXX:1(181) (1975), 253–254

[2] A. N. Parshin, “Abelevy nakrytiya arifmeticheskikh skhem”, DAN SSSR, 243:4 (1978), 855–858 | MR | Zbl

[3] Z. I. Borevich, I. R. Shafarevich, Teoriya chisel, izd-vo “Nauka”, Moskva, 1972 | MR

[4] A. Veil, Osnovy teorii chisel, izd-vo “Mir”, Moskva, 1972 | MR

[5] Algebraicheskaya teoriya chisel, sbornik statei pod redaktsiei Dzh. Kasselsa i A. Frelikha, izd-vo “Mir”, Moskva, 1969 | MR

[6] A. N. Parshin, “K arifmetike dvumernykh skhem. I. Raspredeleniya i vychety”, Izv. AN SSSR, seriya matem., 40 (1976), 736–773 | Zbl

[7] J. P. Serre, “Sur les corps locaux à corps résiduel algébriquement clos”, Bull. Soc. math. France, 89 (1961), 105–154 | MR | Zbl