Avatars of Tate homology


Tate homology and cohomology originated in the realm of group algebras, and the theories generalize to Iwanaga-Gorenstein rings in a straightforward manner. The cohomological theory has a more far-reaching generalization to the setting of associative rings; it is now called stable cohomology, and it agrees with Tate homology over Iwanaga-Gorenstein rings. On the homological side, the picture is not this clear. In the talk I will discuss recent work - joint with Olgur Celikbas, Li Liang, and Grep Piepmeyer - on that topic.