相对于余挠对的复形的Tate上同调

Tate Cohomology of Complexes with Respect to Cotorsion Pairs

设(X,Y)是Abel范畴A中的完备遗传的余挠对.定义了Gorenstein复形范畴G(Y)的Tate余分解,并且给出了相对于G(Y)的Tate上同调的定义,此外,还研究了相对于余挠对(X,Y)的复形的相对上同调和Tate上同调之间的相互关系.

Let(X,Y)be a complete and hereditary cotorsion pair in a bicomplete abelian category A.We give definition of Gorenstein category G(Y)of complexes and Tate-coresolution,and the definition of Tate cohomology with respect to G(Y)is given.In addition,we also study the interaction between the corresponding relative and Tate cohomologies of complexes with respect to the cotorsion pairs.