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Signed-Selmer Groups over the ℤ2p-extension of an Imaginary Quadratic Field

Published online by Cambridge University Press:  20 November 2018

Byoung Du (B. D.) Kim
Byoung Du (B. D.) Kim*
Affiliation:
Victoria University of Wellington. e-mail: bdkimster@gmail.com
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Abstract

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Let $E$ be an elliptic curve over $\mathbb{Q}$ that has good supersingular reduction at $p\,>\,3$ . We construct what we call the $\pm /\pm $ -Selmer groups of $E$ over the $\mathbb{Z}_{p}^{2}$ -extension of an imaginary quadratic field $K$ when the prime $p$ splits completely over $K/\mathbb{Q}$ , and prove that they enjoy a property analogous to Mazur's control theorem.

Furthermore, we propose a conjectural connection between the $\pm /\pm $ -Selmer groups and Loeffler's two-variable $\pm /\pm $ - $p$ -adic $L$ -functions of elliptic curves.

Keywords

11D4511P5511T55elliptic curvesIwasawa theory

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 66 , Issue 4 , 01 August 2014 , pp. 826 - 843
Copyright
Copyright © Canadian Mathematical Society 2014

References

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