The structure sheaf 
of a scheme 
is the sheaf of rings that
assigns to each open set 
the ring 
of regular functions
on 
.
For an affine scheme 
, the structure sheaf is characterized on the principal
open sets
 |
by 
,
where 
and 
is the localization obtained by inverting 
. Together, the underlying topological
space and the structure sheaf make a scheme a locally
ringed space.
