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Gras-Type Conjectures Fattitle for Function Fields

Published online by Cambridge University Press:  04 December 2007

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

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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.

Keywords

Special values of abelian L-functionsunitsclass groupscharacteristic p global fieldsChinburg‘s Ω$_3$-Conjecture.

Information

Type
Research Article
Information
Compositio Mathematica , Volume 118 , Issue 3 , September 1999 , pp. 263 - 290
Copyright
© 1999 Kluwer Academic Publishers