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The parity conjecture for elliptic curves at supersingular reduction primes

2007
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Compositio Mathematica
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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. Introduction In number

doi:10.1112/s0010437x06002569
fatcat:ys3uzict4fc2lcnxdxdvs3jxlq