Nikolai Durov has developed a generalization of conventional scheme theory in which commutative algebraic monads replace commutative unital rings as the basic algebraic objects. The resulting geometry is expressive enough to encompass conventional scheme theory, tropical algebraic geometry and geometry over the field with one element. It also permits the construction of important Arakelov theoretical objects, such as the completion \Spec Z of Spec Z. In this thesis, we prove a projective bundle theorem for the eld with one element and compute the Chow rings of the generalized schemes Sp\ec ZN, appearing in the construction of \Spec Z.