Étale cohomology of a scheme 
is defined using its small étale site 
. The objects are étale
morphisms 
,
and a covering of 
is a family of étale morphisms 
whose images cover 
. Morphisms between these objects
are morphisms of schemes
over 
.
A sheaf 
of Abelian groups on this
site assigns a group 
to each object, with restriction maps and unique gluing of compatible local sections
(Milne 2013, pp. 38-39 and 42).
For such a sheaf 
, the étale cohomology groups are the right derived
functors of the global-section functor 
:
 |
where 
is a nonnegative integer and 
. In particular, 
is the Abelian
group of global sections (Milne 2013, p. 64).
