On the asymptotics of elementary-abelian extensions of local and global function fields

2024/08/29 by Potthast, Nicolas · 2 citations
#11R45 (Primary) 11R37 #11S31 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2408.16394

Abstract

We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic p. For local and rational function fields, we also give precise formulae for the number of elementary-abelian extensions with a fixed discriminant divisor, which describe a local-global principle.

Cited by

• Multivariate counting of wild abelian extensions
• Lifts of unramified twists and local-global principles

Related

• Counting two-step nilpotent wildly ramified extensions of function fields
• Equidistribution for abelian extensions of global fields
• On the density of abelian l-extensions
• Multivariate counting of wild abelian extensions
• Lifts of unramified twists and local-global principles