We extend to the supersingular case the Λ -adic Euler system method (where Λ 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 Q with supersingular reduction at a prime p≥ 5 , we prove results on the Λ -corank of certain plus/minus p-primary Selmer groups à la Kobayashi of E over the anticyclotomic Zp-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 Zp-extension. These theorems can be alternatively obtained by combining results of Nekovář, Vatsal and Iovita–Pollack, but do not seem to be directly available in the current literature.

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

Stefano Vigni
2019

Abstract

We extend to the supersingular case the Λ -adic Euler system method (where Λ 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 Q with supersingular reduction at a prime p≥ 5 , we prove results on the Λ -corank of certain plus/minus p-primary Selmer groups à la Kobayashi of E over the anticyclotomic Zp-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 Zp-extension. These theorems can be alternatively obtained by combining results of Nekovář, Vatsal and Iovita–Pollack, but do not seem to be directly available in the current literature.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/896915
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