Author: J.P.C.Greenlees Title: ``Tate cohomology in axiomatic stable homotopy theory.'' Length: 18 pp Abstract: Any smashing localization gives in an axiomatic stable homotopy theory in the sense of Hovey-Palmieri-Strickland gives rise to a Tate theory. Various known versions of Tate cohomology (for example in commutative algebra, in the cohomology of groups, in equivariant homotopy theory and in chromatic stable homotopy theory) are considered from this point of view. Status: Submitted for publication.