Existence of Gorenstein projective resolutions

Details Existence of Gorenstein projective resolutions Existence of Gorenstein projective resolutions

2004-11-18

arxiv.org/abs/math/0411410v1

Mathematics

Rings and Algebras

21 pages. Supersedes math.RA/0312263 and math.RA/0402176

Scientific paper

Gorenstein rings are important to mathematical areas as diverse as algebraic geometry, where they encode information about singularities of spaces, and homotopy theory, through the concept of model categories. In consequence, the study of Gorenstein rings has led to the advent of a whole branch of homological algebra, known as Gorenstein homological algebra. This paper solves one of the open problems of Gorenstein homological algebra by showing that so-called Gorenstein projective resolutions exist over quite general rings, thereby enabling the definition of a Gorenstein version of derived functors. An application is given to the theory of Tate cohomology.

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