A Bass equality for Gorenstein injective dimension of modules finite over homomorphisms

2019/02/16 by Christensen, Lars Winther, Wu, Dejun
#13D05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.06017

Abstract

Let R → S be a local ring homomorphism and N a finitely generated S-module. We prove that if the Gorenstein injective dimension of N over R is finite, then it equals the depth of R.

Related

• Transfer of Gorenstein dimensions along ring homomorphisms
• Gorenstein dimension of modules over homomorphisms
• Gorenstein injective dimension, Bass formula and Gorenstein rings
• Gorenstein injective dimension and a generalization of Ischebeck Formula
• G-dimension over local homomorphisms. Applications to the Frobenius endomorphism