Gorenstein Duality and Universal Coefficient Theorems

TL;DR

This paper explores a duality in cohomology theories akin to Gorenstein rings, establishing a universal coefficient theorem for torsion modules over Gorenstein spectra, linking cohomology and homology.

Contribution

It introduces a Gorenstein duality framework for cohomology theories and proves a universal coefficient theorem for modules over Gorenstein ring spectra.

Findings

Establishes a duality for cohomology theories with Gorenstein coefficients.

Proves a universal coefficient theorem for torsion modules over Gorenstein spectra.

Connects cohomology and homology via Gorenstein duality.

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)=\Sigma^a Hom( R_*(X), Z/p^{\infty}). A corresponding statement for modules over a commutative Gorenstein ring spectrum is also proved. [Minor typographical and bibliographic changes to the last version.]