Let k be a finitely generated fields of positive characteristic p>0.

Let E be an ordinary elliptic curve over k with a non torsion, non zero, rational point x.By the kummer sequence we get a map:

ϕ:E(k)→lim←nE(k)[pn]E(k)→lim←nH1flat(k,E[pn])→H1(Γk,Tp(E))where Tp(E) is lim←nE(ksep)[pn].

Is it possible to say that ϕ(x) is non zero and non torsion? If not, is it possible find some condition on E or k to ensure this?

If think it is always true that the image of x is non torsion in lim←nH1flat(k,E[pn]).

**Answer**

**Attribution***Source : Link , Question Author : Emiliano Ambrosi , Answer Author : Community*