Operations in étale and motivic cohomology

Reduced Power Operations in Motivic Cohomology

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...

1 Reduced power operations in motivic cohomology

Karoubi’s Construction for Motivic Cohomology Operations

We use an analogue of Karoubi’s construction [4] in the motivic situation to give some cohomology operations in motivic cohomology. We prove many properties of these operations, and we show that they coincide, up to some nonzero constants, with the reduced power operations in motivic cohomology originally constructed by Voevodsky [12]. The relation of our construction to Voevodsky’s is, roughly...

Comparison of Motivic and simplicial operations in mod-l-motivic and étale cohomology

In this paper we explore the relationships between the motivic and simplicial cohomology operations defined on mod-l motivic cohomology. We also explore similar relationships in étale cohomology and conclude by considering certain operations that commute with proper push-forwards.