Gorenstein dimension of modules over homomorphisms

2005/04/16 by Christensen, Lars Winther, Iyengar, Srikanth
#13D05 #13D25 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0504340

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 | Tor^R_m(E,N) \noteq 0 where E is the injective hull of the residue field of R. This result is analogous to a theorem of André on flat dimension.

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