本项目研究稳定同调理论，并借助稳定同调研究Gorenstein微分分次代数，继而给出稳定同调理论在微分分次代数中的应用。我们将研究稳定同调与Mislin的完全同调之间的内在联系，进而给出稳定同调的泛性质并解决Triulzi的问题“完全同调是否是同调函子”；将研究稳定（完全）同调与Tate同调之间的关系，并借此研究Holm猜测“所有的Gorenstein投射模都是Gorenstein平坦的”；将借助稳定同调的vanishing性刻画同调维数有限及Gorenstein同调维数有限的模，继而给出环的同调刻画；将借助稳定同调给出Gorenstein微分分次代数的刻画，进而揭示Gorenstein微分分次代数的同调性。上述研究对于进一步丰富和发展同调代数理论，特别是（上）同调理论具有重要的意义。

In this project, we study stable homology theory, and study Gorenstein differential graded algebras using stable homology, which will give applications of stable homology in differential graded algebra. We will study the relationship between stable homology and Mislin's complete homology, and then give a universal property for stable homology and solve the Triulzi's question whether complete homology is a homological functor. We will study the relationship between stable (complete) homology and Tate homology, and then further study the Holm conjecture which claims that all Gorenstein projective modules are Gorenstein flat. We will give some characterizations of modules of finite (Gorenstein) homological dimension using vanishing of stable homology, and then give homological characterizations of rings. We will give some characterizations of Gorenstein differential graded algebras using stable homology, and then describe homological properties of Gorenstien differential graded algebras. The above studies are important for further enriching and developing homological algebra and (co)homology theory.