Governing fields for hyperelliptic function fields

arXiv (Cornell University)

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 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.

Authors 1

1. Joppe Stokvis corresponding Aachen Mathematical Institute

   Leiden University · QuSoft

   Affiliation as printed

   Mathematical Institute , Leiden University and QuSoft , Amsterdam ,