On the non-vanishing of generalized Kato classes for elliptic curves of rank $2$

Francesc Castella, Ming-Lun Hsieh

We prove the first cases of a conjecture by Darmon--Rotger on the non-vanishing of generalized Kato classes attached to elliptic curves $E$ over $\mathbf{Q}$ of rank $2$. Our metho…