Let $E$ be a elliptic curve without complex multiplication over a number field $F$. Let $F_n=F[E_{p^n}]$ and $F_{\infty}=F[E_{p^\infty}]$. So by a well know theorem of Serre, the Galois group $Gal(F_\infty/F)$ is an open subgroup of $GL_2(\mathbb{Z}_p)$.

Consider the natural norm maps on $E_{p^\infty}(F_m)$. I read somewhere that for $m$ sufficiently large, these maps are essentially just multiplication by $p^4$ and so the projective limit of the inverse system $E_{p^\infty}(F_m)$ is zero.

I don't know the proof of this. Can anyone provide me with a proof? That will be very helpful.