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arXiv · 2005.10920

Galois covers of $\mathbb{P}^1$ and number fields with large class groups

Jean Gillibert·Pierre Gillibert
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Abstract

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.

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Jean Gillibert, Pierre Gillibert. 2020-05-21. Galois covers of $\mathbb{P}^1$ and number fields with large class groups. https://arxiv.org/abs/2005.10920

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