Compositio Mathematica

Gras-Type Conjectures Fattitle for Function Fields

a1 Department of Mathematics, University of Texas at Austin, Austin, TX 78712-1082, USA; e-mail:

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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 Ω$_3$-Conjecture on the Galois module structure of the group of S-units, for cyclic extensions of prime degree of function fields.

Key Words: Special values of abelian L-functions; units; class groups; characteristic p global fields; Chinburg‘s Ω$_3$-Conjecture..