Geodesic
On the Brauer Group of a Two-Dimensional Local Field
Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 838-841 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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