论文标题
减少算术曲线的非平地锥
Nonsplit conics in the reduction of an arithmetic curve
论文作者
论文摘要
对于代数函数字段$ f/k $和一个离散估值$ v $ $ k $，带有完美的残留率$ k $，我们将$ f $ fort的离散估值数量限制为$ f $ v $，其残留场是$ k $的零属属的代数函数字段，但没有裁定。假设$ k $在$ f $中相对在代数相对封闭，我们发现，$ v $ to $ v $至$ f $的非划定剩余的超验扩展的数量由$ \ mathfrak {g}+1 $界定，其中$ \ mathfrak {g mathfrak {g} $是$ f/k $的属。出现了曲线功能字段中的正方和算法的应用程序。
For an algebraic function field $F/K$ and a discrete valuation $v$ of $K$ with perfect residue field $k$, we bound the number of discrete valuations on $F$ extending $v$ whose residue fields are algebraic function fields of genus zero over $k$ but not ruled. Assuming that $K$ is relatively algebraically closed in $F$, we find that the number of nonruled residually transcendental extensions of $v$ to $F$ is bounded by $\mathfrak{g}+1$ where $\mathfrak{g}$ is the genus of $F/K$. An application to sums of squares in function fields of curves over $\mathbb{R}(\!(t)\!)$ is presented.
