Gorenstein categories and Tate cohomology on projective schemes

Details Gorenstein categories and Tate cohomology on projective schemes Gorenstein categories and Tate cohomology on projective schemes

2007-11-07

arxiv.org/abs/0711.1181v1

Mathematics

Category Theory

to appear in Mathematische Nachrichten (accepted in June'06)

Scientific paper

We study Gorenstein categories. We show that such a category has Tate cohomological functors and Avramov-Martsinkovsky exact sequences connecting the Gorenstein relative, the absolute and the Tate cohomological functors. We show that such a category has what Hovey calls an injective model structure and also a projective model structure in case the category has enough projectives. As examples we show that if X is a locally Gorenstein projective scheme then the category Qco(X) of quasi-coherent sheaves on $X$ is such a category and so has these features.

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