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The parity conjecture for elliptic curves at supersingular reduction primes

Published online by Cambridge University Press:  19 January 2007

Byoung Du (B. D.) Kim
Byoung Du (B. D.) Kim
Affiliation:
Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, [email protected]
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Abstract

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In number theory, the Birch and Swinnerton-Dyer (BSD) conjecture for a Selmer group relates the corank of a Selmer group of an elliptic curve over a number field to the order of zero of the associated $L$-function $L(E, s)$ at $s=1$. We study its modulo two version called the parity conjecture. The parity conjecture when a prime number $p$ is a good ordinary reduction prime was proven by Nekovar. We prove it when a prime number $p>3$ is a good supersingular reduction prime.

Keywords

elliptic curveBSD conjectureIwasawa theory11G05
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 1 , January 2007 , pp. 47 - 72
Copyright
Foundation Compositio Mathematica 2007