Counting torsors for wild abelian groups

TL;DR

This paper investigates the enumeration of G-torsors over global fields of characteristic p, focusing on specific height functions for finite abelian p-groups, extending previous theoretical frameworks.

Contribution

It introduces new methods for counting G-torsors over global fields using height functions, advancing the understanding of torsor distribution in positive characteristic.

Findings

Derived explicit formulas for counting G-torsors

Extended height-based counting techniques to new classes of abelian p-groups

Provided theoretical insights into torsor distribution over global fields

Abstract

Let $F$ be a global field of characteristic $p > 0$ and $G$ a finite abelian $p$-group. In this paper we treat the question of counting $G$-torsors over $F$ for certain heights developed in [DY25].