The generalized Coates-Sinnott Conjecture for some families of cubic extensions of number fields
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<p>Let E/<em>k</em> be an <em>S</em><sub>3</sub> extension of totally real number fields with quadratic subextension<em> F</em>/k. The generalized Coates-Sinnott conjecture predicts that for n ≥ 2, the integralized Stickelberger element <em>w</em><sub>n</sub>(<em>E</em>)<em>θ<sub>E/F</sub></em>(1-n) attached to the cyclic cubic extension<em> E</em>/F should annihilate the <em>p</em>-part of <em>H<sup>2</sup><sub>Μ</sub></em>(<em>Ο<sub>E</sub></em>, Z(<em>n</em>)) for all primes <em>p</em>. We show this to be true for all p ≠ 2, 3.</p>