On the K-theory spectrum of a ring of algebraic integers, by W. G. Dwyer and S. A. Mitchell
Let l be an odd prime number, R the ring of l-integers in an algebraic
number field, and KR the algebraic K-theory spectrum of R. (The word
spectrum is used here in the sense of stable homotopy theory.) We give
a simple formula for the l-adic topological K-theory of KR, in terms
of standard number theoretic invariants of R. This formula leads to
many other things. A few of them are:
There are similar results if R is replaced by an l-adic local field.
- An explicit recipe for using classical invariants of R to
construct a candidate C for the algebraic K-theory spectrum of R. If
the Lichtenbaum/Quillen conjecture is true, then C essentially is the
algebraic K-theory spectrum. The spectrum C is constructed from the
arithmetic of R in a way which extends Quillen's construction of
FPsi(q) from the Galois theory of a finite field F(q).
- Calculations in some cases of the l-adic topological K-theory of
- Conjectural calculations of the mod l cohomology of BGL(R). These
calculations are contingent on the Quillen/Lichtenbaum conjecture.
W. G. Dwyer <firstname.lastname@example.org>
S. A. Mitchell <email@example.com>