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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.

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If $p:X \times \mathbb P^n \rightarrow \mathbb P^n$ is the natural projection, then $Z$ corresponds to $p^* \mathcal O(1)$. Also, $\{x_0 \} \times \mathbb P^n \cong \mathbb P^n$ and the pullback of a line bundle is a line bundle, so the second statement follows as well since all line bundles on projective look like $\mathcal O(k)$ for some integer $k$.