Let $K$ be the function field of a curve $C$ over a $p$-adic field $k$. We prove that, for each $n,d\ge 1$ and for each hypersurface $Z$ in ${\mathbb{P}}_K^n$ of degree $d$ with $d^2\le n$, the second Milnor $K$-theory group of $K$ is spanned by the images of the norms coming from finite extensions $L$ of $K$ over which $Z$ has a rational point. When the curve $C$ has a point in the maximal unramified extension of $k$, we generalize this result to hypersurfaces $Z$ in ${\mathbb{P}}_K^n$ of degree $d$ with $d\le n$.

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关于 p-adic 曲线函数场 Milnor K2 的 Kato 和 Kuzumaki 性质

让$K$是曲线的函数场$C$在...之上$p$-adic场$k$。我们证明，对于每个$n,d\ge 1$对于每个超曲面$Z$在${\mathbb{P}}_K^n$学位的$d$和$d^2\le n$, 第二个米尔诺$K$- 理论组$K$被来自有限扩展的规范图像所跨越$L$的$K$在之上$Z$有其合理性。当曲线$C$在最大无分支扩展中有一个点$k$，我们将这个结果推广到超曲面$Z$在${\mathbb{P}}_K^n$学位的$d$和$d\le n$。