I have a question on Joseph Silverman's book ``Advanced topics in the arithmetic of elliptic curves’’ (1999 printing). I asked him; he answered that he doesn't know off-hand and suggested that I put it as a question on MathOverflow, which I am doing now.

On p. 251, he defines a subgroup $E(K)_0$ of the group of points of an elliptic curve $E$ over the function field $K$ of a curve $C/k$: the Néron-Tate height pairing is integral when restricted to this subgroup. In Rem. 9.4.1, he says that it will be studied in detail in the next chapter, referring to (IV.6.12), (IV.9.1), (IV.9.2) and exercise 4.25. I hope that $E(K)_0$ is $\mathcal{E}^0(C)$, where $\mathcal{E}$ is the Néron model of $E$ and $\mathcal{E}^0$ is its identity component. But

IV.6.12 does not exist; IV.9.2 mentions a subgroup $E_0(K)$ which is indeed equal to $\mathcal{E}^0(R)$, but the situation is local ($R$ is a dvr) and I cannot find something comparing it to $E(K)_0$ (the definitions are not obvious to compare, at least for me!)

Is the answer to my hope `yes', and can one deduce it from what is in his book?