Geodesic
On the Brauer Group of a Two-Dimensional Local Field
Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 838-841.

Voir la notice de l'article provenant de la source Math-Net.Ru

The two-dimensional local field $K=F_q((u))((t))$, $\operatorname{char}K=p$, and its Brauer group $\operatorname{Br}(K)$ are considered. It is proved that, if $L=K(x)$ is the field extension for which we have $x^p-x=ut^{-p}=:h$, then the condition that $(y,f\,|\,h]_K=0$ for any $y\in K$ is equivalent to the condition $f\in\operatorname{Im}(\operatorname{Nm}(L^*))$.
Keywords: two-dimensional local field, Brauer group, field extension, local field. 
@article{MZM_2007_81_6_a2,
     author = {M. A. Dubovitskaya},
     title = {On the {Brauer} {Group} of a {Two-Dimensional} {Local} {Field}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {838--841},
     publisher = {mathdoc},
     volume = {81},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a2/}
}
TY  - JOUR
AU  - M. A. Dubovitskaya
TI  - On the Brauer Group of a Two-Dimensional Local Field
JO  - Matematičeskie zametki
PY  - 2007
SP  - 838
EP  - 841
VL  - 81
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a2/
LA  - ru
ID  - MZM_2007_81_6_a2
ER  - 
%0 Journal Article
%A M. A. Dubovitskaya
%T On the Brauer Group of a Two-Dimensional Local Field
%J Matematičeskie zametki
%D 2007
%P 838-841
%V 81
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a2/
%G ru
%F MZM_2007_81_6_a2
M. A. Dubovitskaya. On the Brauer Group of a Two-Dimensional Local Field. Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 838-841. http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a2/

[1] A. N. Parshin, “Kogomologii Galua i gruppa Brauera lokalnykh polei”, Teoriya Galua, koltsa, algebraicheskie gruppy i ikh prilozheniya, Tr. MIAN, 183, 1990, 159–169 | MR | Zbl

[2] A. N. Parshin, “Lokalnaya teoriya polei klassov”, Algebraicheskaya geometriya i ee prilozheniya, Tr. MIAN, 165, 1984, 143–170 | MR | Zbl

[3] J.-P. Serre, Corps Locaux, Deuxième édition. Publications de l'Université de Nancago, VIII, Hermann, Paris, 1968 | MR | Zbl