Level Raising mod 2 and Obstruction to Rank Lowering

  title={Level Raising mod 2 and Obstruction to Rank Lowering},
  author={Chao Li},
  journal={International Mathematics Research Notices},
  • Chao Li
  • Published 24 April 2019
  • Mathematics
  • International Mathematics Research Notices
Given an elliptic curve E defined over Q, we are motivated by the 2-part of the Birch and Swinnerton-Dyer formula to study the relation between the 2-Selmer rank of E and the 2Selmer rank of an abelian variety A obtained by Ribet’s level raising theorem. For certain imaginary quadratic fields K satisfying the Heegner hypothesis, we prove that the 2-Selmer ranks of E and A over K have different parity, as predicted by the BSD conjecture. When the 2-Selmer rank of E is one, we further prove that… 
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