Gorenstein dimension of modules over homomorphisms

Given a homomorphism of commutative noetherian rings R→SR→S and an SS-module NN, it is proved that the Gorenstein flat dimension of NN over RR, when finite, may be computed locally over SS. When, in addition, the homomorphism is local and NN is finitely generated over SS, the Gorenstein flat dimension equals sup{m∈Z∣TormR(E,N)≠0}, where EE is the injective hull of the residue field of RR. This result is analogous to a theorem of André on flat dimension.