An invertible sheaf on a scheme 
is a sheaf 
of 
-modules such that every point
has an open neighborhood 
for which 
is isomorphic to 
as an 
-module. Equivalently, it is a
locally free sheaf of 
-modules of rank 1.
Isomorphism classes of invertible sheaves form a group under the tensor product,
called the Picard group of 
. The ideal sheaf of an effective
Cartier divisor is invertible.
