Lambda operations, K-theory and motivic cohomology, by Marc Levine

This is a two-part paper: in part one, we give a construction of natural lambda operations satisfying the special lambda ring identities on the relative K-groups with support K_p^W(Y; D_1,..., D_n), where Y is a noetherian scheme with an ample family of line bundles, W is a closed subset, and D_1, ... D_n are closed subschemes. In part two, we apply this construction to give a relation of K-theory an motivic cohomology, after inverting "small" primes. In particular, we have natural isomophisms

CH^q(X,p)\cong gr^q_\gamma K_p(X)

after inverting (d+p-1)!, where X is a smooth quasi-projective variety of dimension d over a field k.

Marc Levine <>