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2 results

  • The parity conjecture for elliptic curves at supersingular reduction primes

  • Byoung Du (B. D.) Kim
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 1 / January 2007
    Published online by Cambridge University Press:
    19 January 2007, pp. 47-72
    Print publication:
    January 2007
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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.