Article

# The Rubin-Stark Conjecture For Imaginary Abelian Fields Of Odd Prime Power Conductor

12/2001;
Source: CiteSeer

ABSTRACT We build upon ideas developed in [9], as well as results of Greither on a strong form of Brumer's Conjecture ([2]--[4]), and prove Rubin's integral version of Stark's Conjecture for imaginary abelian extensions of Q of odd prime power conductor.

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##### Article:On a refined Stark Conjecture for function fields
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ABSTRACT: We prove that a refinement of Stark's Conjecture formulated by Rubin in [14] is true up to primes dividing the order of the Galois group, for finite, abelian extensions of function fields over finite fields. We also show that in the case of constant field extensions a statement stronger than Rubin's holds true. 0.
10/2000;

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### Keywords

Brumer's Conjecture

odd prime power conductor

Rubin's integral version

Stark's Conjecture

strong form