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Stark's question and a refinement of Brumer's conjecture extrapolated to the function field case

Published online by Cambridge University Press:  04 December 2007

Cristian D. Popescu
Cristian D. Popescu
Affiliation:
University of California, San Diego, Department of Mathematics, 9500 Gilman Drive, La Jolla, CA 92093-0112, USAcpopescu@math.ucsd.edu
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Abstract

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We show that the extrapolation to the case of global fields of characteristic p of a question posed by Stark in 1980, regarding abelian L-functions of order of vanishing 2 at s = 0, has a negative answer. We provide links between various versions of Stark's question and a natural refinement of Brumer's conjecture, in the general context of global fields of arbitrary characteristic. As a consequence, we show that the refinement of Brumer's conjecture is, in general, false for characteristic p global fields.

Keywords

special values of L-functionsStickelberger elementsideal-class groupsgroups of unitsmultiplicative Galois module structure11R4211R5811R27
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 3 , May 2004 , pp. 631 - 646
Copyright
Foundation Compositio Mathematica 2004