Chevalley-Weil Theorem and Subgroups of Class Groups

Yuri Bilu; Jean Gillibert

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arXiv · 1606.03128

Chevalley-Weil Theorem and Subgroups of Class Groups

Yuri Bilu·Jean Gillibert

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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.

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Yuri Bilu, Jean Gillibert. 2016-06-09. Chevalley-Weil Theorem and Subgroups of Class Groups. https://arxiv.org/abs/1606.03128

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