Joint IAS/Princeton University Number Theory Seminar

Studying the Selmer groups of elliptic curves for a supersingular prime is difficult. It turned out we should instead use the plus/minus Selmer groups defined by Kobayashi. In this talk, we will see the plus/minus Selmer group theory for supersingular primes is very analogous to the Selmer group theory for ordinary primes, and as an application, we will prove the parity conjecture of elliptic curves for supersingular primes among other things. We will report some other recent progress as well.