Chevalley-Weil Theorem and Subgroups of Class Groups
Number Theory
2017-09-26 v2
Abstract
We prove, under some mild hypothesis, that an \'etale cover of curves defined over a number field has infinitely many specializations into an everywhere unramified extension of number fields. This constitutes an "absolute" version of the Chevalley-Weil theorem. Using this result, we are able to generalize the techniques of Mestre, Levin and the second author for constructing and counting number fields with large class group.
Cite
@article{arxiv.1606.03128,
title = {Chevalley-Weil Theorem and Subgroups of Class Groups},
author = {Yuri Bilu and Jean Gillibert},
journal= {arXiv preprint arXiv:1606.03128},
year = {2017}
}
Comments
Minor improvements following the referee's suggestions. To appear in Israel J. of Math