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    Burungale, Ashay A. 2017. ON THE NON-TRIVIALITY OF THE -ADIC ABEL–JACOBI IMAGE OF GENERALISED HEEGNER CYCLES MODULO , II: SHIMURA CURVES. Journal of the Institute of Mathematics of Jussieu, Vol. 16, Issue. 01, p. 189.

    Nekovář, Jan 2015. Compatibility of arithmetic and algebraic local constants (the case ). Compositio Mathematica, Vol. 151, Issue. 09, p. 1626.

    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.

    Nekovář, Jan 2013. Some consequences of a formula of Mazur and Rubin for arithmetic local constants. Algebra & Number Theory, Vol. 7, Issue. 5, p. 1101.

    Dokchitser, Tim and Dokchitser, Vladimir 2011. Root numbers and parity of ranks of elliptic curves. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2011, Issue. 658,

    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.

    VIRDOL, CRISTIAN 2011. ON MAZUR'S CONJECTURE FOR TWISTED L-FUNCTIONS OF ELLIPTIC CURVES OVER TOTALLY REAL OR CM FIELDS. Glasgow Mathematical Journal, Vol. 53, Issue. 01, p. 207.

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On the parity of ranks of Selmer groups IV. With an appendix by Jean-Pierre Wintenberger

  • Jan Nekovář (a1)
Abstract
Abstract

We prove the parity conjecture for the ranks of p-power Selmer groups (p⁄=2) of a large class of elliptic curves defined over totally real number fields.

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COPYRIGHT: © Foundation Compositio Mathematica 2009
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[6] T. Dokchitser and V. Dokchitser , Parity of ranks for elliptic curves with a cyclic isogeny, J. Number Theory 128 (2008), 662–679.
[10] R. Greenberg , Trivial zeros of p-adic L-functions, Contemp. Math. 165 (1994), 149–173.
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[17] B. Mazur and K. Rubin , Growth of Selmer rank in nonabelian extensions of number fields, Duke Math. J. 143 (2008), 437–461.
[18] P. Monsky , Generalizing the Birch–Stephens theorem. I. Modular curves, Math. Z. 221 (1996), 415–420.
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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
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