Adams Operations for Bivariant K-Theory and a Filtration Using Projective Lines
Mark E. Walker · K-Theory · 2000
. We establish the existence of Adams operations on the members of a filtration of K-theory which is defined using products of projective lines. We also show that this filtration induces the gamma filtration on the rational K-groups of a smooth variety over a field of characteristic zero. Key words: K-theory, Adams operations, gamma filtration, motivic cohomology 1. Introduction In [8], Grayson studies a filtration on the K-theory spectrum of a regular ring R whose t th stage is defined by considering the category of projective R-modules equipped with t-tuples of pairwise commuting automorphisms. By a filtration, we mean a sequence of maps of spec- Partially supported by the National Science Foundation, grant #DMS-9627754. 2 Mark E. Walker tra : : : \\Gamma! GW t+1 (R) \\Gamma! GW t (R) \\Gamma! : : : \\Gamma! GW 0 (R) = K(R) together with fibration sequences GW t+1 (R) \\Gamma! GW t (R) \\Gamma! GW t=t+1 (R): The filtration studied by Grayson has the additional propert...