Gorenstein dimension of modules over homomorphisms
Abstract
Given a homomorphism of commutative noetherian rings R --> S and an S-module N, it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated over S, the Gorenstein flat dimension equals supm | TorRm(E,N) 0 where E is the injective hull of the residue field of R. This result is analogous to a theorem of Andr\'e on flat dimension.
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