### Two-primary algebraic K-theory of rings of integers in number fields, by John Rognes and Chuck Weibel

We relate the algebraic K-theory of a totally real number field F
to its étale cohomology. We also relate it to the zeta-function of
F when F is Abelian. This establishes the two-primary part of the
`Lichtenbaum conjectures.' To do this we compute the two-primary
K-groups of F and of its ring of integers, using recent results of
Voevodsky and the Bloch-Lichtenbaum spectral sequence, modified for
finite coefficients in an appendix. A second appendix, by M. Kolster,
explains the connection to the zeta-function and Iwasawa theory.

This paper has appeared in *Journal of the AMS* 13 (2000), 1-54.

John Rognes <rognes@math.uio.no>

Chuck Weibel <weibel@math.rutgers.edu>