We investigate Tate cohomology of modules over a commutative noetherian ring with
respect to semidualizing modules. We identify classes of modules admitting Tate resolutions …

We consider two preenveloping classes of left R-modules ℐ, ℰ such that Inj⊂ ℐ⊂ ℰ, and a
left R-module N. For any left R-module M and n≥ 1 we define the relative extension …

We construct local Tate cohomology groups H ̂∗ I (A; M) of an A-module M at a finitely
generated ideal I by splicing together the Grothendieck local cohomology groups [16] with …

We introduce and study" quasidualizing" modules over a commutative local noetherian ring
R. An artinian R-module T is quasidualizing if the homothety map [special characters …

We compare and contrast various relative cohomology theories that arise from resolutions
involving semidualizing modules. We prove a general balance result for relative …

For complexes of modules we study two new constructions which we call the pinched tensor
product and the pinched Hom. They provide new methods for computing Tate homology …

Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …

This paper is a sequel to [L. Positselski, Dedualizing complexes and MGM duality, J. Pure
Appl. Algebra 220 (12)(2016) 3866–3909, arXiv: 1503.05523 [math. CT]; Contraadjusted …

In this paper, we investigate the maximal Cohen–Macaulay property of tensor products of
modules, and then give criteria for projectivity of modules in terms of vanishing of Ext …

Motivated by the classical structure of Tate cohomology, we develop and study a Tate
cohomology theory in a triangulated category C. Let E be a proper class of triangles. By …