Gras-Type Conjectures for Function Fields

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 $\Omega_3$--Conjecture on the Galois module structure of the group of $S$--units, for cyclic extensions of prime degree of function fields.