Governing fields for hyperelliptic function fields

Joppe Stokvis

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arXiv · 2505.20117

Governing fields for hyperelliptic function fields

Joppe Stokvis

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Abstract

We study the 8-rank of class groups of hyperelliptic function fields and show that such 8-ranks are governed by splitting conditions in so-called governing fields. A similar result was proven for quadratic number fields by Stevenhagen, who used a theory of R\'edei symbols and R\'edei reciprocity to do so. We introduce a version of the R\'edei reciprocity law for function fields and use this to show existence of governing fields.

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Joppe Stokvis. 2025-05-26. Governing fields for hyperelliptic function fields. https://arxiv.org/abs/2505.20117

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