The ℓ-parity conjecture over the constant quadratic extension

@article{Cesnavicius2017TheC,
  title={The ℓ-parity conjecture over the constant quadratic extension},
  author={Kestutis Cesnavicius},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2017},
  volume={165},
  pages={385 - 409}
}
  • Kestutis Cesnavicius
  • Published 2017
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
Abstract For a prime ℓ and an abelian variety A over a global field K, the ℓ-parity conjecture predicts that, in accordance with the ideas of Birch and Swinnerton–Dyer, the ℤℓ-corank of the ℓ∞-Selmer group and the analytic rank agree modulo 2. Assuming that char K > 0, we prove that the ℓ-parity conjecture holds for the base change of A to the constant quadratic extension if ℓ is odd, coprime to char K, and does not divide the degree of every polarisation of A. The techniques involved in the… Expand
8 Citations
p-Selmer growth in extensions of degree p
PSP volume 165 issue 3 Cover and Back matter
  • Mathematical Proceedings of the Cambridge Philosophical Society
  • 2018