论文标题
在Kato和Kuzumaki的Milnor $ k_2 $ p $ - adic曲线的功能字段的属性上
On Kato and Kuzumaki's properties for the Milnor $K_2$ of function fields of $p$-adic curves
论文作者
论文摘要
让$ k $是$ p $ - adic字段$ k $的曲线$ c $的功能字段。我们证明，对于每个$ n，d \ geq 1 $，对于每个hypersurface $ z $ in $ \ mathbb {p}^n_ {n_ {k} $，$ d $ d $ a $ d^2 \ leq n $，第二个$ k $的第二个$ k $的$ k $ a $ $ k $ $ k $ k $ k $ k y limitations $ k k in limity $ k k in limentions $ k $ k k in of z $ k $ k $ k k $ k $ k k in o n of z $ k k $ k k $ k。当曲线$ c $在$ k $的最大未施加扩展中有一个点时，我们将此结果推广到$ \ mathbb {p}^n_ {k} $ d $ d $的HyperSurfaces $ z $，带有$ d \ d \ d \ d \ leq n $。
Let $K$ be the function field of a curve $C$ over a $p$-adic field $k$. We prove that, for each $n, d \geq 1$ and for each hypersurface $Z$ in $\mathbb{P}^n_{K}$ of degree $d$ with $d^2 \leq n$, 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 $\mathbb{P}^n_{K}$ of degree $d$ with $d \leq n$.
