# Existence oof Gorenstein Projective Resolutions and tate cohomology – University of Copenhagen

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# Existence oof Gorenstein Projective Resolutions and tate cohomology

Specialeforsvar ved Anne Hoff Kjeldsen Lützen

Titel: Existence of Gorenstein Projective Resolutions and Tate cohomology

Abstract: In this thesis I prove existence of proper Gorenstein projective resolutions and Tate cohomology over rings with a dualizing complex. The thesis is based on Peter Jørgensen's article "Existence of Gorenstein projective resolutions and Tate cohomology". Using Bousfield Localization, I prove that the inclusion functor, of the full subcategory of complete projective resolutions in the homotopy category of projective modules, has a right adjoint over rings with a dualizing complex. It is proven that existence of this right adjoint functor implies existence of Gorenstein projective resolutions and Tate cohomology groups.

Vejleder:  Henrik G. Holm
Censor:    Niels Lauritzen, Aarhus Universitet