On the nonvanishing of generalised Kato classes for elliptic curves of rank 2
Journal
Forum of Mathematics, Sigma
Journal Volume
10
Date Issued
2022
Author(s)
Abstract
Let E/Q be an elliptic curve and p > 3 be a good ordinary prime for E and assume that L(E, 1)=0 with root number+1 (so ords=1 L(E, s) ≥ 2)). A construction of Darmon-Rotger attaches to E and an auxiliary weight 1 cuspidal eigenform g such that L(E, ad(g), 1) ≠ =0, a Selmer class κp ∈ Sel(Q,VpE), and they conjectured the equivalence {equation presented} In this article, we prove the first cases on Darmon-Rotger's conjecture when the auxiliary eigenform g has complex multiplication. In particular, this provides a new construction of nontrivial Selmer classes for elliptic curves of rank 2. ©
Type
journal article