论文标题
功能字段的相对班级第一问题，iii
The relative class number one problem for function fields, III
论文作者
论文摘要
我们在有限字段上完成了曲线功能字段的相对类别第一问题的解决方案。利用来自两篇早期论文的工作，这将减少到在$ \ mathbb {f} _2 $上找到40个规定的weil多项式的所有功能字段。然后，可以直接验证这些字段中的三个字段通过微不足道的相对阶层组接收到无处不在的二次扩展。搜索是通过基于brill的曲线仔细枚举曲线进行的 - 这些属中曲线的模量空间，尤其是Mukai对开放层的描述。
We complete the solution of the relative class number one problem for function fields of curves over finite fields. Using work from two earlier papers, this reduces to finding all function fields of genus 6 or 7 over $\mathbb{F}_2$ with one of 40 prescribed Weil polynomials; one may then verify directly that three of these fields admit an everywhere unramified quadratic extension with trivial relative class group. The search is carried out by carefully enumerating curves based on the Brill--Noether stratification of the moduli spaces of curves in these genera, and particularly Mukai's descriptions of the open strata.
