On a problem \`a la Kummer-Vandiver for function fields

TL;DR

This paper constructs counterexamples to a Kummer-Vandiver type problem in function fields using Artin-Schreier base change, challenging previous assumptions in the area.

Contribution

It introduces a novel method employing Artin-Schreier base change to produce counterexamples in the context of function fields.

Findings

Counterexamples to Kummer-Vandiver type questions in function fields

Demonstrates limitations of previous conjectures in the function field setting

Uses Artin-Schreier base change as a key technique

Abstract

We use Artin-Schreier base change to construct counterexamples to a Kummer-Vandiver type question for function fields.