Stable operations on complex $K$-theory

Adams Operations on Higher Arithmetic K-theory

We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The definition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soulé, by means of the homotopy groups of the homotopy fiber of the regulator map. They are compatible with the Adams operations on algebraic K-theory. The definition re...

Adams Operations on Higher K - Theory 3

We construct Adams operations on higher algebraic K-groups induced by operations such as symmetric powers on any suitable exact category, by constructing an explicit map of spaces, combinatorially deened. The map uses the S-construction of Waldhausen, and deloops (once) earlier constructions of the map.

Exterior Power Operations on Higher K-theory

Adams Operations on Higher K-theory

We construct Adams operations on higher algebraic K-groups induced by operations such as symmetric powers on any suitable exact category, by constructing an explicit map of spaces, combinatorially defined. The map uses the S-construction of Waldhausen, and deloops (once) earlier constructions of the map.

Lambda operations, K theory and motivic cohomology

This paper is in two parts: in part one, our main object is to give a construction of natural λ-operations for relative K-theory with supports, satisfying the special λ-ring identities. In the second part, we give an application to the relation of motivic cohomology and algebraic K-theory of a smooth quasi-projective variety over a field. The main idea in the construction of the λ-operations is...