### Bott elements in algebraic K-theory, by Bruno Kahn

In this paper, we associate to every closed subgroup G of the group of
l-adic units a certain "cyclotomic" spectrum. When the prime l is odd, or
when l=2 and G consists of units congruent to 1 mod 4, we map the
zero-space of this spectrum to the zero-space of the algebraic K-theory
spectrum of any connected scheme X over Z[1/l] such that the image of the
l-adic cyclotomic character associated to X equals G. This is the basis of the
construction of "anti-Chern classes" from etale cohomology to algebraic
K-theory (see "On the Lichtenbaum-Quillen conjecture", Algebraic K-theory
and algebraic topology (P.G Goerss, J.F. Jardine, eds), NATO ASI Series,
Ser. C 407 (1993), 147-166).

This is a revised and much expanded version of a 1993 Paris 7 preprint.

This has now been published in Topology 36 (1997), 963-1006.
Click here.

Bruno Kahn <kahn@mathp7.jussieu.fr>