This construction is a global version of the construction of the divisor class group, or ideal class group, and is much used in algebraic geometry and the theory of complex manifolds.
For complex manifolds the exponential sheaf sequence gives basic information on the Picard group.
The name is in honour of Émile Picard's theories, in particular of divisors on algebraic surfaces.
The construction of a scheme structure on (representable functor version of) the Picard group, the Picard scheme, is an important step in algebraic geometry, in particular in the duality theory of abelian varieties.
In the cases of most importance to classical algebraic geometry, for a non-singular complete variety V over a field of characteristic zero, the connected component of the identity in the Picard scheme is an abelian variety called the Picard variety and denoted Pic0(V).
The quotient Pic(V)/Pic0(V) is a finitely-generated abelian group denoted NS(V), the Néron–Severi group of V. In other words, the Picard group fits into an exact sequence The fact that the rank of NS(V) is finite is Francesco Severi's theorem of the base; the rank is the Picard number of V, often denoted ρ(V).