Let $A$ be an abelian variety over a number field $K$. Let $\mathcal{A}$ be the Neron model of $A$ over $O_K$. Let $\Omega_{\mathcal{A}/O_K}$ be the sheaf of invariant differential forms on $\mathcal{A}$.

In the formulation of the Tamagawa Number Conjecture for abelian varieties, for e.g., page 13 of the following paper http://arxiv.org/abs/math/0507275, we have to take an integral basis for the Lie algebra $Lie(\mathcal{A})$ in order to compute the period, which is the determinant of the isomorphism $\alpha_{A} : H_B^+(A)_{\mathbb{R}} \to Lie(A)_{\mathbb{R}}$.

In that paper, where $K=\mathbb{Q}$, the author just takes a $\mathbb{Z}$-basis of $Hom_{\mathbb{Z}}(\Omega_{\mathcal{A}/O_K}(\mathcal{A}),\mathbb{Z})$ as the integral basis for $Lie(A)$. I guess you can do this because $Hom_{\mathbb{Z}}(\Omega_{\mathcal{A}/O_K}(\mathcal{A}),\mathbb{Z})$ is a free $\mathbb{Z}$-module.

My question is that in general when $K\neq \mathbb{Q}$ and $\Omega_{\mathcal{A}/O_K}(\mathcal{A})$ is not a free $O_K$-module but only a projective $O_K$-module, how can we take an integral basis for $Lie(A)$ ?

Thank you very much.