2025-05-26
Governing fields for hyperelliptic function fields
Publication
Publication
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 Rédei symbols and Rédei reciprocity to do so. We introduce a version of the Rédei reciprocity law for function fields and use this to show existence of governing fields.
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| doi.org/10.48550/arXiv.2505.20117 | |
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Stokvis, J. (2025). Governing fields for hyperelliptic function fields. doi:10.48550/arXiv.2505.20117 |
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