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Paper   IPM / M / 8432
School of Mathematics
  Title:   Cohomology theories for complexes
1.  J. Asadollahi
2.  Sh. Salarian
  Status:   Published
  Journal: J. Pure Appl. Algebra
  Vol.:  210
  Year:  2007
  Pages:   771–787
  Supported by:  IPM
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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