Let $X$ be a noetherian, integral, separated scheme which is regular in codimension one. One can prove $X\times \mathbb{P}^n$ is also has these properties (Here the fiber product is over Spec($\mathbb{Z}$), and that $\mathbb{P}^n$ is the same as $\mathbb{P}_\mathbb{Z}^n$). Let $Z=X\times \mathbb{P}^n-X\times \mathbb{A}^n$, one can prove $Z=X\times \mathbb{P}^{n-1}$, and that $Z$ is a closed, irreducible subscheme of codimension one. So $[Z]\in Cl(X\times \mathbb{P}^n)$, the Weil class group.
I want to prove $[Z]$ is torsion free by the following way:
Let $x_0\in X$, so from $i: \{x_0\}\times \mathbb{P}^n \hookrightarrow X\times \mathbb{P}^n$, we have $Cl(\{x_0\}\times \mathbb{P}^n) \to Cl(X\times \mathbb{P}^n)$. I want to prove:
(1) $[Z]$ corresponds to an invertible sheaf $L$;
(2) $i^*L$ is isomorphic to some $O(k)$. Thus $[Z]$ is torsion free.
But for (1), I don't know how to write down $L$ explicitly (it doesn't seem doable following the definition); for (2), I don't know what $i^*L$ should be.