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Global Sections of the Identity Component of Neron model

First, a remark: the free part of $A(K)$ is a quotient, not a sub, and so it is possible that a point of infinite order in $A(K)$ could have non-trivial image in $\Phi_A(X)$. Probably what you mean …
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Maps on the identity components of Neron models

If I'm not mistaken, the map $Res^0$ is a bijection. Indeed, restriction induces maps $$Hom_X(\mathcal A,\mathcal B) \to Hom_X(\mathcal A^0,\mathcal B^0)\to Hom_K(A,B).$$ The composite is a bijectio …
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