On the Eisenstein ideal over function fields

The concept of the Eisenstein ideal in Hecke algebras of classical
modular curves was introduced by Mazur in the 1970's.
As was demonstrated by Mazur, Ribet, Wiles and others, the Eisenstein ideal
provides a powerful tool in many arithmetic problems over number fields.

We will discuss the analogue of the Eisenstein ideal in the context of
Drinfeld modular curves, and some of its applications to
the study of rational torsion subgroups, component groups and cuspidal divisor
groups of Jacobians of Drinfeld modular curves.