The Gras conjecture in function fields by Euler systems

TL;DR

This paper proves the Gras conjecture for groups generated by Stark units in global function fields using Euler systems derived from Drinfel'd modules, extending classical techniques from number theory.

Contribution

It introduces a novel application of Euler systems from Drinfel'd modules to prove the Gras conjecture in the context of function fields.

Findings

Proves the Gras conjecture for specific groups in function fields.

Constructs Euler systems from torsion points of Drinfel'd modules.

Extends classical number theory techniques to function field setting.

Abstract

We use Euler systems to prove the Gras conjecture for groups generated by Stark units in global function fields. The techniques applied here are classical and go back to Thaine, Kolyvagin and Rubin. We obtain our Euler systems from the torsion points of sign-normalized Drinfel'd modules.