The Koszul Complex and Duality

This paper is basically about local, Cohen-Macaulay rings although many of the theorems are more general in nature. The major tool that we shall use is the Koszul complex and its self duality. The Koszul complex is closely linked with the functors Γ and λ which we shall define presently. Our main results will be the computation of the derived functors of Γ and λ.