Gorenstein Cohomology And Tate Cohomology In Exact Categories

Let A be an exact category with enough projectives and injectives.In this thesis,we first show that if A is weakly idempotent complete and also has countable direct sums and direct products,then sup{GpdA | A ?A}=sup{GidA | A ? A}.We call the common value of the quantities the global Gorenstein dimension of A.Secondly,the Gorenstein cohomology ExtGPn(-,-)and ExtGIn(-,-)in A are introduced,and we show that for any object A in A with finite Gorenstein projec-tive dimension and any object B in A with finite Gorenstein injective dimension,ExtGPn(A,B)?ExtGIn(A,B).Thirdly,if A is weakly idempotent complete,we build an A-M type long exact sequence in A connecting Gorenstein cohomology,cohomol-ogy and Tate cohomology.Finally,we show that Tate cohomology in A is balanced.