Another example: If $X$ is a smooth projective variety over a field $k$, then the relative Picard functor is representable by a smooth group scheme $Pic_{X/k}$. This is the moduli space of line bundles on $X$, in particular $Pic_{X/k}(k)$ (Edit: If $X(k)\neq \emptyset$) is the usual Picard group. The geometry of the Picard scheme tells us a lot about the line bundles; for example one can look at the connected component $Pic_{X/k}^0$ of the identity of $Pic_{X/k}$, and the points $L\in Pic_{X/k}^0(k)$ are precisely the line bundles belonging to divisors algebraically equivalent to $0$0$. 1 Another example: If$X$is a smooth projective variety over a field$k$, then the relative Picard functor is representable by a smooth group scheme$Pic_{X/k}$. This is the moduli space of line bundles on$X$, in particular$Pic_{X/k}(k)$is the usual Picard group. The geometry of the Picard scheme tells us a lot about the line bundles; for example one can look at the connected component$Pic_{X/k}^0$of the identity of$Pic_{X/k}$, and the points$L\in Pic_{X/k}^0(k)$are precisely the line bundles belonging to divisors algebraically equivalent to$0\$