The Leray spectral sequence relates cohomology of sheaves on two ringed spaces.
For a morphism 
of ringed spaces and
a sheaf 
of 
-modules, it has
 |
Here 
is the direct-image functor, 
is its 
th right derived functor,
and 
. It is a Grothendieck
spectral sequence for the composition of the direct-image functor
and the global-sections functor. A version also applies
to bounded below complexes of 
-modules (The Stacks Project Authors
2026).
