We prove that if f:R → S is a local homomorphism of noetherian local rings of finite flat dimension and M is a non-zero finitely generated S-module whose Gorenstein flat dimension over R is bounded by the difference of the embedding dimensions of R and S, then M is a totally reflexive S-module and f is an exceptional complete intersection map. This is an extension of a result of Brochard, Iyengar, and Khare to Gorenstein flat dimension. We also prove two analogues involving Gorenstein injective dimension.
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Hossein Faridian (2024) studied this question.
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