Symmetry in vanishing of Tate cohomology over Gorenstein rings

2016/08/16 by Arash Sadeghi, Sadeghi, Arash
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.1608.04588

openalex publication_date 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate symmetry in the vanishing of Tate cohomology for finitely generated modules over local Gorenstein rings. For finitely generated R-modules M and N over Gorenstein local ring R, it is shown that \widehatExtⁱ_R(M,N)=0 for all i∈ℤ if and only if \widehatExtⁱ_R(N,M)=0 for all i∈ℤ.

Related

• On vanishing of generalized local cohomology modules
• Vanishing of cohomology over Gorenstein rings of small codimension
• Symmetry theorems for Ext vanishing
• Nonvanishing cohomology and classes of Gorenstein rings
• Generalized local cohomology modules and homological Gorenstein dimensions