Gorenstein projective dimension for complexes

Veliche, Oana

doi:10.1090/S0002-9947-05-03771-2

Gorenstein projective dimension for complexes
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Trans. Amer. Math. Soc. 358 (2006), 1257-1283 Request permission

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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