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Gorenstein dimension of modules over homomorphisms

Lars Winther Christensen·Srikanth Iyengar
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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 sup{m | 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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Lars Winther Christensen, Srikanth Iyengar. 2005-11-18. Gorenstein dimension of modules over homomorphisms. https://arxiv.org/abs/math/0504340

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