Related to the divisor class group.

The divisor class group embeds into the Picard group: \begin{align*} 0 \to \textrm{Pic}(X) \to \textrm{Cl}(X) \to \bigoplus_{x \in \textrm{Sing}(X)} \textrm{Cl}(\mathcal{O}_{X,x}) \to H^2(X, \mathcal{O}_X^{\ast}) \to 0. \end{align*}

Relation to divisor class group:

When \(X\) is a variety, \({\operatorname{CH}}_{\dim X - 1} X \cong \operatorname{Div} \operatorname{Cl} (X)\), the divisor class group. If $X\in {\mathsf{sm}}{\mathsf{Var}}_{/ {k}} $, then \({\operatorname{CH}}_{\dim X - 1}X \cong \operatorname{Pic}(X)\), the Picard group.