Governing fields for hyperelliptic function fields

2025/05/26 by Joppe Stokvis, Stokvis, Joppe
Computer Science · Economics, Econometrics and Finance · #11R11 (Primary) #11R58 #11R65 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2505.20117

openalex publication_date 2025/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Joint distribution of spins
• The 2-primary class group of certain hyperelliptic curves
• Quadratische K�rper im Gebiete der h�heren Kongruenzen. I.

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