K4(Z) is the trivial group, by John Rognes

We prove that the fourth algebraic K-group of the rational integers is the trivial group. The argument is based on a spectrum level rank filtration of the algebraic K-theory spectrum, uses group homology calculations to determine the rank three stage of this filtration, and concludes with convergence results established in the present paper.

Note added August 24th, 1995: The author has found an error in this paper, which affects the proof of the main result stated in the title. Proposition 2.2 and Theorem 2.3 only hold as stated when the ring R is a field, and this affects the main connectivity result Proposition 5.2, which is used to conclude the main theorem. The preprint will be kept on this server, to facilitate any further work to repair this error.

John Rognes <rognes@math.uio.no>