In this note, we show that the algebraic K-theory of generalized archimedean
valuation rings occurring in Durov's compactification of the spectrum of a
number ring is given by stable homotopy groups of certain classifying spaces.
We also show that the "residue field at infinity" is badly behaved from a
K-theoretic point of view.Comment: Final version. To appear in Journal of Homotopy and Related
Structure
