Cohomology class of a non torsion point

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)limnE(k)[pn]E(k)limnH1flat(k,E[pn])H1(Γk,Tp(E))

where Tp(E) is limnE(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 limnH1flat(k,E[pn]).

Answer

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

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