**Yoshifumi Tsuchimoto**

Note that a sequence

of sheaves of abelian groups is exact if and only if it is exact stalkwise.

- For any open subset
of
, the corresponding sequence

In a language of category theory, the global section function

(Sheaf of abelian groups on $X$) (Ab)

is a left exact functior. (But not exact.) To treat it, we employ derived functors.

- For any ring , if an -module is injective, then the associated sheaf on is injective.
- The category ( -modules) has enough injectives.
- For any scheme
with an affine open covering
,
for any
-quasi coherent sheaf
on
, we have:
: injective injective for any .

for