On the local-global divisibility of torsion points on elliptic curves and ${\mathrm{GL}}_2$-type varieties

Florence Gillibert, Gabriele Ranieri

Let $p$ be a prime number and let $k$ be a number field. Let $E$ be an elliptic curve defined over $k$. We prove that if $p$ is odd, then the local-global divisibility by any power…