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 <>