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September 2011 Stickelberger elements and Kolyvagin systems
Kâzım Büyükboduk
Nagoya Math. J. 203: 123-173 (September 2011). DOI: 10.1215/00277630-1331890

Abstract

In this paper, we construct (many) Kolyvagin systems out of Stickelberger elements utilizing ideas borrowed from our previous work on Kolyvagin systems of Rubin-Stark elements. The applications of our approach are twofold. First, assuming Brumer’s conjecture, we prove results on the odd parts of the ideal class groups of CM fields which are abelian over a totally real field, and we deduce Iwasawa’s main conjecture for totally real fields (for totally odd characters). Although this portion of our results has already been established by Wiles unconditionally (and refined by Kurihara using an Euler system argument, when Wiles’s work is assumed), the approach here fits well in the general framework the author has developed elsewhere to understand Euler/Kolyvagin system machinery when the core Selmer rank is r>1 (in the sense of Mazur and Rubin). As our second application, we establish a rather curious link between the Stickelberger elements and Rubin-Stark elements by using the main constructions of this article hand in hand with the “rigidity” of the collection of Kolyvagin systems proved by Mazur, Rubin, and the author.

Citation

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Kâzım Büyükboduk. "Stickelberger elements and Kolyvagin systems." Nagoya Math. J. 203 123 - 173, September 2011. https://doi.org/10.1215/00277630-1331890

Information

Published: September 2011
First available in Project Euclid: 18 August 2011

zbMATH: 1257.11099
MathSciNet: MR2834252
Digital Object Identifier: 10.1215/00277630-1331890

Subjects:
Primary: 11R23, 11R42
Secondary: 11R27, 11R29, 11R34

Rights: Copyright © 2011 Editorial Board, Nagoya Mathematical Journal

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Vol.203 • September 2011
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