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| Paper IPM / M / 8432 |
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| Abstract: | |||||
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We introduce and study a complete cohomology theory for complexes, which provides an extended version of Tate- Vogel cohomology to the setting of (arbitrary) complexes over associative rings. For complexes of finite Gorenstein projective dimension a notion of relative Ext is introduced. Based on these co homology groups, some homological invariants of modules over commutative noetherian local rings, such as Martsinkovsky's (-invariants and relative and Tate version of Betti numbers, are extended to the framework of complexes with finite homology. The relation of these invariants with their prototypes is explored.
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