Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes

Abstract

We extend to the supersingular case the $$\Lambda $$ -adic Euler system method (where $$\Lambda $$ is a suitable Iwasawa algebra) for Heegner points on elliptic curves that was originally developed by Bertolini in the ordinary setting. In particular, given an elliptic curve E over $$\mathbb {Q}$$ with supersingular reduction at a prime $$p\ge 5$$ , we prove results on the $$\Lambda $$ -corank of certain plus/minus p-primary Selmer groups a la Kobayashi of E over the anticyclotomic $$\mathbb {Z}_p$$ -extension of an imaginary quadratic field and on the asymptotic behaviour of p-primary Selmer groups of E when the base field varies over the finite layers of such a $$\mathbb {Z}_p$$ -extension. These theorems can be alternatively obtained by combining results of Nekovař, Vatsal and Iovita–Pollack, but do not seem to be directly available in the current literature.