2024/02/09 by Faridian, Hossein
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2402.06834
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.