On the parity of ranks of Selmer groups

(Un exposé de Jan Nekovar au séminaire de théorie des nombres de Chevaleret le 19 mars 2001)

Résumé :

Let E be an elliptic curve over Q with good ordinary reduction at a prime p. We show that the parity of the (co)-rank of the p-Selmer group of E is as predicted by the conjecture of Birch and Swinnerton-Dyer.