Chevalley-Weil Theorem and Subgroups of Class Groups
arXiv:1606.03128
Abstract
We prove, under some mild hypothesis, that an étale 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.
Minor improvements following the referee's suggestions. To appear in Israel J. of Math