Motivic cohomology of cyclic coverings

Abstract: Cyclic coverings produce many examples of topologically contractible smooth affine complex varieties. In this paper, we study the motivic cohomology groups of cyclic coverings over algebraically closed fields of characteristic $0$. In particular, we prove that in many situations Chow groups of cyclic coverings become trivial after tensoring with $\mathbb{Q}$. Furthermore, we can prove that the Chow groups of certain bicyclic coverings are trivial even without tensoring with $\mathbb{Q}$.