Kummer map of an elliptic curve
= Kummer map of an elliptic curve
= Kummer maps of an elliptic curve
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The map is a connecting homomorphism from the multiplication exact sequence. Its image is constrained by the local conditions defining the <Selmer group of an elliptic curve>.
The multiplication-by-$n$ sequence gives an injective connecting map
$$
E(K)/nE(K)\hookrightarrow H^1(K,E[n]).
$$
Local conditions restrict its image to the finite $n$-Selmer group.