A quasi-coherent sheaf on a scheme 
is a sheaf 
of 
-modules, where 
is the structure sheaf,
such that on every open subscheme 
that is an affine scheme,
its restriction is isomorphic
to 
for a unital R-module 
. Here 
is the associated sheaf: on the
open set 
, its sections
form 
,
the localization of 
obtained by inverting 
(The Stacks Project Authors 2026).
The association 
translates algebraic constructions on modules into geometric
constructions on sheaves. In particular, quasi-coherent
ideal sheaves correspond to closed
subschemes.
