Algebraic K-theory of rings of integers in local and global fields, by Charles A. Weibel

This is a survey describing the algebraic $K$-groups of local and global fields, and the $K$-groups of rings of integers in these fields. We have used the result of Rost and Voevodsky to determine the odd torsion in these groups.

Most of the results in this survey have appeared in various places over the last three decades, usually prefaced with assumptions which we no longer need. One new result is the verification that when n=2 mod 4 the finite groups Kn(Z) are cyclic for n<20,000; conjecturally the bound on n is unnecesary.

A revised and renumbered version of this paper appeared as chapter 5 (pp. 139-184) in the book Handbook of $K$-theory, Springer-Verlag, 2005.


Charles A. Weibel <weibel@math.rutgers.edu>