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THE PLUS/MINUS SELMER GROUPS FOR SUPERSINGULAR PRIMES

Published online by Cambridge University Press:  07 June 2013

BYOUNG DU KIM
BYOUNG DU KIM*
Affiliation:
Victoria University of Wellington, Wellington 6140, New Zealand email bdkim@msor.vuw.ac.nz
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Abstract

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Suppose that an elliptic curve $E$ over $ \mathbb{Q} $ has good supersingular reduction at $p$. We prove that Kobayashi’s plus/minus Selmer group of $E$ over a ${ \mathbb{Z} }_{p} $-extension has no proper $\Lambda $-submodule of finite index under some suitable conditions, where $\Lambda $ is the Iwasawa algebra of the Galois group of the ${ \mathbb{Z} }_{p} $-extension. This work is analogous to Greenberg’s result in the ordinary reduction case.

Keywords

elliptic curvesIwasawa theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 2 , October 2013 , pp. 189 - 200
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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