  We relate cohomology defined by a system of local Lagrangian with the
cohomology class of the system of local variational Lie derivative, which is in
turn a local variational problem; we show that the latter cohomology class is
zero, since the variational Lie derivative `trivializes' cohomology classes
defined by variational forms. As a consequence, conservation laws associated
with symmetries ensuring the vanishing of the second variational derivative of
a local variational problem are globally defined.
