Gras-Type Conjectures Fattitle for Function Fields

Based on results obtained in [15], we construct groups of special S-units for function fields of characteristic p>0, and show that they satisfy Gras-type Conjectures. We use these results in order to give a new proof of Chinburg's ₃-Conjecture on the Galois module structure of the group of S-units, for cyclic extensions of prime degree of function fields.