Some Problems In Gorenstein Derived Category

The notion of Derived Category was introduced by A.Grothendieck and J.L.Verdier in 1960s.It obtain enormous success in Algebraic Geometry and The Representation in Algebra.Gao Nan and Zhang Pu introduced Gorenstein Derived Category in 2010.They acquire many important consequences about this new concept.And then Gao Nan continues her investigation in Gorenstein Derived Category.She works a lot of consequences about A-R triangle,Gorenstein Derived equivalence and Recollement.This paper consists three parts.In first part we introduce some fundamental concepts about derived Category and Homological Algebra.In second part we introduce two equivalent definition of Gorenstein Derived Category,and define the concept of Gorenstein Derived Functor.Giving a sufficient condition for this functor' exists.In third part we get several conclusions which generalize the classical consequences in derived category.We first obtain the following:Theorem 3.1.9 If a trifunctor ?:g((?))?D(?)(A)is dense,then(?)((?))-dimA<?,in this(?)is a contravariant subcategory of A.Moreover we also give a sufficient and necessary condition for the exist of A-R triangle in a bounded Gorenstein derived category of a finite dimensional algebra.We consider CM-finite algebra's derived equivalence and give a Gornestein derived category's recollement.