In this note we explore the relationships between the motivic cohomology operations and the (classical) cohomology operations defined on mod-l étale cohomology. More precisely we show that the cohomology operations on motivic cohomology transform to the (classical) cohomology operations on mod-l étale cohomology upon inverting the motivic Bott element.

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.