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The Rubin–Stark conjecture for a special class of function field extensions

✍ Scribed by Cristian D. Popescu

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
362 KB
Volume
113
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 k p∞ := k p • k ∞ of the maximal pro-p abelian extension k p /k and the maximal constant field extension k ∞ /k of k, which happens to sit inside the maximal abelian extension k ab 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).

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