论文标题
$ \ Mathbb {p}^1 $的Galois封面和带有大型组的数字字段
Galois covers of $\mathbb{P}^1$ and number fields with large class groups
论文作者
论文摘要
对于每个有限的子组$ g $的$ pgl_2（\ mathbb {q}）$，对于每个整数$ n $ coprime至$ 6 $，我们明确地构建了无限的无限无限的galois扩展名，$ \ mathbb {q} $的$ \ mathbb {q} $与group $ g $ ang group $ g $，其理想的类别$ n $ $ n $ $ $ $ \＃g-1。这提供了新的$ n $ rank记录，用于数字字段的课程组。
For each finite subgroup $G$ of $PGL_2(\mathbb{Q})$, and for each integer $n$ coprime to $6$, we construct explicitly infinitely many Galois extensions of $\mathbb{Q}$ with group $G$ and whose ideal class group has $n$-rank at least $\#G-1$. This gives new $n$-rank records for class groups of number fields.
