  In his thesis, N. Durov develops a theory of algebraic geometry in which
schemes are locally determined by commutative algebraic monads. In this
setting, one is able to construct the Arakelov geometric compactification of
the spectrum of the ring of integers in a purely algebraic fashion. This object
arises as the limit of a certain projective system of generalized schemes. We
study the constituents of this projective system, and compute their algebraic
K-theory.
