论文标题
功能字段的相对班级第一问题，i
The relative class number one problem for function fields, I
论文作者
论文摘要
我们将具有相同类号码的功能场（曲线上的曲线）的有限扩展分类为有限计算；在所有情况下都完成此计算，除非两条曲线都有基本场$ \ Mathbb {f} _2 $和属$> 1 $;并在其余案例中给出一个猜想的答案。猜想将在随后的论文中解决。
We reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field $\mathbb{F}_2$ and genus $>1$; and give a conjectural answer in the remaining cases. The conjecture will be resolved in subsequent papers.
