Geodesic
Orders of topological generators of the $K$-group of a standard two-dimensional local field
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 17, Tome 356 (2008), pp. 118-148 
O. Yu. Ivanova. Orders of topological generators of the $K$-group of a standard two-dimensional local field. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 17, Tome 356 (2008), pp. 118-148. http://geodesic.mathdoc.fr/item/ZNSL_2008_356_a3/
@article{ZNSL_2008_356_a3,
     author = {O. Yu. Ivanova},
     title = {Orders of topological generators of the $K$-group of a~standard two-dimensional local field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {118--148},
     year = {2008},
     volume = {356},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_356_a3/}
}
TY  - JOUR
AU  - O. Yu. Ivanova
TI  - Orders of topological generators of the $K$-group of a standard two-dimensional local field
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2008
SP  - 118
EP  - 148
VL  - 356
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2008_356_a3/
LA  - ru
ID  - ZNSL_2008_356_a3
ER  - 
%0 Journal Article
%A O. Yu. Ivanova
%T Orders of topological generators of the $K$-group of a standard two-dimensional local field
%J Zapiski Nauchnykh Seminarov POMI
%D 2008
%P 118-148
%V 356
%U http://geodesic.mathdoc.fr/item/ZNSL_2008_356_a3/
%G ru
%F ZNSL_2008_356_a3

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider the topological $K$-group of a complete, weakly unramified over the constant subfield, two-dimensional local field of mixed characteristic and with finite second residue field. We estimate the orders of natural generators of this group from above and from below, and prove some relations between these orders. Bibl. – 10 titles.

[1] V. G. Boitsov, I. B. Zhukov, “Prodolzhimost tsiklicheskikh rasshirenii polnykh diskretno normirovannykh polei”, Zap. nauchn. semin. POMI, 305, POMI, SPb., 2003, 5–17 | MR

[2] I. B. Zhukov, “Milnorovskie i topologicheskie $K$-gruppy mnogomernykh polnykh polei”, Algebra i analiz, 9:1 (1997), 98–147 | MR | Zbl

[3] I. B. Zhukov, Abelevy rasshireniya i topologicheskie $K$-gruppy mnogomernykh lokalnykh polei, Dis. ... kand. fiz.-matem. nauk, Leningradskii gosudarstvennyi universitet, 1991

[4] O. Yu. Ivanova, “Topologicheskie $K$-gruppy dvumernykh lokalnykh polei”, Zap. nauchn. semin. POMI, 343, POMI, SPb., 2007, 206–221 | MR

[5] I. B. Fesenko, “Teoriya lokalnykh polei. Teoriya polei klassov. Mnogomernaya lokalnaya teoriya polei klassov”, Algebra i analiz, 4:3 (1992), 1–41 | MR | Zbl

[6] I. B. Fesenko, S. V. Vostokov, Local fields and their extensions. A constructive approach, Transl. Math. Monographs, 121, Amer. Math. Soc., Providence, RI, 1993 | MR | Zbl

[7] O. Hyodo, “Wild ramification in the imperfect residue field case”, Galois Representations and Arithmetic Algebraic Geometry (Kyoto, 1985/Tokyo, 1986), Adv. Stud. Pure Math., 12, North-Holland, Amsterdam, 1987, 287–314 | MR

[8] H. Miki, “On $\mathbb Z_p$-extensions of complete $p$-adic power series fields and function fields”, J. Fac. Sci. Univ. Tokyo. Sect. IA Math., 21 (1974), 377–393 | MR | Zbl

[9] S. Vostokov, “Explicit formulas for the Hilbert sympol”, Invitation to Higher Local Fields (Munster, 1999), Geom. Topol. Monogr., 3, Geom. Topol. Publ., Coventry, 2000, 81–89 | MR | Zbl

[10] I. Zhukov, “Higher dimensional local fields”, Invitation to Higher Local Fields (Munster, 1999), Geom. Topol. Monogr., 3, Geom. Topol. Publ., Coventry, 2000, 5–18 | MR | Zbl