Some characterizations of dualizing complexes in terms of G_C-dimension

2023/05/17 by Majid Rahro Zargar, Zargar, Majid Rahro
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2305.10244

openalex publication_date 2023/05/17 · openalex created_date 2023/05/21 · openalex updated_date 2026/07/28

Abstract

Let (R,\fm) be a local ring and C be a homologically bounded and finitely generated R-complex. Then, we prove that C is a dualizing complex of R if and only if C is a Cohen-Macaulay semidualizing complex of type one or μ_R^{inf C+dim_R(C)} (\fm,R)=β_{inf C}^R(C). Also, we show that a semidualizing complex C is dualizing if and only if there exists a type one Cohen-Macaulay R-module of finite G_C-dimension or there exists a type one Cohen-Macaulay R-complex of finite G_C-dimension such that dim_R(X)=dim_R(C)-\gr_C(X). Furthermore, for a semidualizing R-complex C, we prove that C∼ R if and only if there exists a type one Cohen-Macaulay R-module M which belongs to the Auslander class A_C(R).

Related

• Dual of Bass numbers and dualizing modules
• Numerical aspects of complexes of finite homological dimensions
• Characterizing local rings via homological dimensions and regular sequences
• Presentations of rings with non-trivial semidualizing modules
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