论文标题
功能字段的相对班级第一问题，ii
The relative class number one problem for function fields, II
论文作者
论文摘要
我们确定，属的功能场的任何有限扩展大于1，其相对阶层是微不足道的是galois和循环。这取决于前面论文的结果，该论文建立了两个字段的可能的多项式列表的有限列表。鉴于此列表，我们通过计算扩展中低度位置分裂的选项来分析大多数案例，然后考虑这些选项对Galois关闭Jacobian的某些同等因素的Weil多项式的影响。在一种情况下，我们改用基于原理极化的分析，以豪的论点为基础。
We establish that any finite extension of function fields of genus greater than 1 whose relative class group is trivial is Galois and cyclic. This depends on a result from a preceding paper which establishes a finite list of possible Weil polynomials for both fields. Given this list, we analyze most cases by computing options for the splittings of low-degree places in the extension, then consider the effect of these options on the Weil polynomials of certain isogeny factors of the Jacobian of the Galois closure. In one case, we use instead an analysis based on principal polarizations, modeled on an argument of Howe.
