GRAS-TYPE CONJECTURES FOR FUNCTION FIELDS

CRISTIAN D. POPESCU

Abstract. Based on results obtained in a companion paper [MSRI preprint 1997-002], 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 Ω_{3}–Conjecture on the Galois module structure of the group of S–units, for cyclic extensions of prime degree of function fields.