  We prove that, for a Poisson vertex algebra V, the canonical injective
homomorphism of the variational cohomology of V to its classical cohomology is
an isomorphism, provided that V, viewed as a differential algebra, is an
algebra of differential polynomials in finitely many differential variables.
This theorem is one of the key ingredients in the computation of vertex algebra
cohomology. For its proof, we introduce the sesquilinear Hochschild and
Harrison cohomology complexes and prove a vanishing theorem for the symmetric
sesquilinear Harrison cohomology of the algebra of differential polynomials in
finitely many differential variables.
