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The Rubin-Stark conjecture for a special class of function field extensions
Authors:Cristian D Popescu
Institution:Department of Mathematics, Department 0112, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0112, USA
Abstract:We prove a strong form of the Brumer-Stark Conjecture and, as a consequence, a strong form of Rubin's integral refinement of the abelian Stark Conjecture, for a large class of abelian extensions of an arbitrary characteristic p global field k. This class includes all the abelian extensions K/k contained in the compositum kp?kp·k of the maximal pro-p abelian extension kp/k and the maximal constant field extension k/k of k, which happens to sit inside the maximal abelian extension kab of k with a quasi-finite index. This way, we extend the results obtained by the present author in (Comp. Math. 116 (1999) 321-367).
Keywords:11R42  11R58  11R27
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