Serreʹs vanishing conjecture for Ext-groups

Let R be a noetherian commutative local ring, and M,N be finitely generated R-modules. Then a generalized form of Serreʹs Vanishing conjecture can be stated as follows: if (1)length (M RN)<∞,(2)pd(M),pd(N)<∞, and(3)dim M+dimN