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    Trihan, Fabien and Yasuda, Seidai 2014. The -parity conjecture for abelian varieties over function fields of characteristic 0$" height="12pt">. Compositio Mathematica, Vol. 150, Issue. 04, p. 507.


    KIM, BYOUNG DU 2013. THE PLUS/MINUS SELMER GROUPS FOR SUPERSINGULAR PRIMES. Journal of the Australian Mathematical Society, Vol. 95, Issue. 02, p. 189.


    Trihan, Fabien and Wuthrich, Christian 2011. Parity conjectures for elliptic curves over global fields of positive characteristic. Compositio Mathematica, Vol. 147, Issue. 04, p. 1105.


    Dokchitser, Tim and Dokchitser, Vladimir 2010. On the Birch-Swinnerton-Dyer quotients modulo squares. Annals of Mathematics, Vol. 172, Issue. 1, p. 567.


    Lei, Antonio 2010. Coleman maps for modular forms at supersingular primes over Lubin–Tate extensions. Journal of Number Theory, Vol. 130, Issue. 10, p. 2293.


    Dokchitser, Tim and Dokchitser, Vladimir 2009. Regulator constants and the parity conjecture. Inventiones mathematicae, Vol. 178, Issue. 1, p. 23.


    DOKCHITSER, TIM and DOKCHITSER, VLADIMIR 2009. Self-duality of Selmer groups. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 146, Issue. 02, p. 257.


    Kim, Byoung Du 2009. The symmetric structure of the plus/minus Selmer groups of elliptic curves over totally real fields and the parity conjecture. Journal of Number Theory, Vol. 129, Issue. 5, p. 1149.


    Nekovář, Jan 2009. On the parity of ranks of Selmer groups IV. With an appendix by Jean-Pierre Wintenberger. Compositio Mathematica, Vol. 145, Issue. 06, p. 1351.


    Lozano-Robledo, Álvaro 2008. Ranks of abelian varieties over infinite extensions of the rationals. manuscripta mathematica, Vol. 126, Issue. 3, p. 393.


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The parity conjecture for elliptic curves at supersingular reduction primes

  • Byoung Du (B. D.) Kim (a1)
  • DOI: http://dx.doi.org/10.1112/S0010437X06002569
  • Published online: 19 January 2007
Abstract

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.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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