Cofiniteness and vanishing of local cohomology modules

Let R be a noetherian local ring with maximal ideal m and residue field k . If M is a finitely generated R -module then the local cohomology modules are known to be Artinian. Grothendieck [3], exposé 13, 1·2 made the following conjecture: If I is an ideal of R and M is a finitely generated R -module, then Hom R ( R / I , ) is finitely generated.