Gorenstein Duality and Universal Coefficient Theorems

2022/06/22 by Davis, Donald M., Greenlees, J. P. C.
#13H10 #18G15 #55N20 #55P43 #55U20 #55U30 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.11391

Abstract

The paper describes a duality phenomenon for cohomology theories with the character of Gorenstein rings. For a connective cohomology theory with the p-local integers in degree 0, and coefficient ring R_* Gorenstein of shift 0, this states that for X with R_*(X) torsion, we have R^*(X)=Σ^a Hom( R_*(X), Z/p^∞). A corresponding statement for modules over a commutative Gorenstein ring spectrum is also proved. [Minor typographical and bibliographic changes to the last version.]

Related

• Gorenstein Homology and Finiteness Properties of Local (Co)homology
• Anderson and Gorenstein duality
• Local duality for the singularity category of a finite dimensional\n Gorenstein algebra
• Existence of Gorenstein projective resolutions
• On modules whose dual is of finite Gorenstein dimension