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On the Iwasawa theory of CM fields for supersingular primes


Author: Kâzım Büyükboduk
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 11G05, 11G07, 11G40, 11R23, 14G10
DOI: https://doi.org/10.1090/tran/7029
Published electronically: August 3, 2017
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Abstract: The goal of this article is two-fold: First, to prove a (two-variable) main conjecture for a CM field $ F$ without assuming the $ p$-ordinary hypothesis of Katz, making use of what we call the Rubin-Stark $ \mathcal {L}$-restricted Kolyvagin systems, which is constructed out of the conjectural Rubin-Stark Euler system of rank $ g$. (We are also able to obtain weaker unconditional results in this direction.) The second objective is to prove the Park-Shahabi plus/minus main conjecture for a CM elliptic curve $ E$ defined over a general totally real field again using (a twist of the) Rubin-Stark Kolyvagin system. This latter result has consequences towards the Birch and Swinnerton-Dyer conjecture for $ E$.


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Additional Information

Kâzım Büyükboduk
Affiliation: Department of Mathematics, Koç University, 34450 Sariyer, Istanbul, Turkey
Address at time of publication: School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
Email: kbuyukboduk@ku.edu.tr

DOI: https://doi.org/10.1090/tran/7029
Keywords: Iwasawa theory, Iwasawa's main conjectures, Rubin-Stark elements
Received by editor(s): December 27, 2013
Received by editor(s) in revised form: October 30, 2014, and May 12, 2016
Published electronically: August 3, 2017
Additional Notes: This work was partially supported by Marie Curie IRG grant EC-FP7 230668, TÜBİTAK grant 113F059, EU Horizon 2020 MC-GF Grant CriticalGZ/745691, and the Turkish Academy of Sciences.
Article copyright: © Copyright 2017 American Mathematical Society