Let
M
M
be an open subset of a Stein manifold without isolated points. Let
Ω
p
{\Omega ^p}
be the sheaf of germs of holomorphic
p
p
-forms on
M
M
. Then
H
q
(
M
,
Ω
p
)
{H^q}(M,{\Omega ^p})
is either
0
0
or else infinite dimensional.
H
q
(
M
,
S
)
{H^q}(M,\mathcal {S})
may be nonzero and finite dimensional if
M
M
is the regular points of a Stein space or if
S
\mathcal {S}
is an arbitrary coherent sheaf over
M
M
.