Parity conjectures for elliptic curves over global fields of positive characteristic

Abstract

We prove the $p$-parity conjecture for elliptic curves over global fields of characteristic $p>3$. We also present partial results on the $\ell$-parity conjecture for primes $\ell \ne p$.

to be published in Compositio Mathematica. This version differs slightly from the one to be published

References in corpus (4)

• Regulator constants and the parity conjecture
• On the Birch-Swinnerton-Dyer quotients modulo squares
• Parity of ranks for elliptic curves with a cyclic isogeny
• Self-duality of Selmer groups