Compositio Mathematica



Gras-Type Conjectures Fattitle for Function Fields


CRISTIAN D. POPESCU a1
a1 Department of Mathematics, University of Texas at Austin, Austin, TX 78712-1082, USA; e-mail: popescu@math.utexas.edu

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Abstract

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..