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Gorenstein projective dimension for complexes

Oana Veliche
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Abstract

We define and study a notion of Gorenstein projective dimension for complexes of left modules over associative rings. For complexes of finite Gorenstein projective dimension we define and study a Tate cohomology theory. Tate cohomology groups have a natural transformation to classical Ext groups. In the case of module arguments, we show that these maps fit into a long exact sequence, where every third term is a relative cohomology group defined for left modules of finite Gorenstein projective dimension.

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Oana Veliche. 2004-06-03. Gorenstein projective dimension for complexes. https://arxiv.org/abs/math/0406057

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