The stalk 
of a sheaf 
on a topological
space 
at a point 
is the direct limit
 |
where 
runs over the open
neighborhoods of 
and the maps are the restriction maps of the sheaf. A section over 
is an element of 
, and the restriction maps compare such elements on smaller
open sets. The stalk records the local behavior of sections arbitrarily near 
.
For the structure sheaf 
of a scheme, the stalk 
is the local ring of 
at 
.
