  We show, in two complementary ways, that D=11 supergravity---in contrast to
all its lower dimensional versions---forbids a cosmological extension. First,
we linearize the putative model about an Anti de Sitter background and show
that it cannot even support a "global" supersymmetry invariance; hence there is
no Noether construction that can lead to a local supersymmetry. This is true
with the usual 4-form field as well as for a "dual", 7-form, starting point.
Second, a cohomology argument, starting from the original full nonlinear
theory, establishes the absence of deformations involving spin 3/2 mass and
cosmological terms. In both approaches, it is the form field that is
responsible for the obstruction. ``Dualizing'' the cosmological constant to an
11-form field also fails.
