Motivic cohomology of cyclic coverings

TL;DR

This paper investigates the motivic cohomology of cyclic coverings, showing that their Chow groups often become trivial over algebraically closed fields of characteristic zero, with some cases trivial without tensoring.

Contribution

It provides new results on the triviality of Chow groups of cyclic coverings and bicyclic coverings, expanding understanding of their motivic cohomology in algebraic geometry.

Findings

Chow groups of cyclic coverings become trivial after tensoring with Q.

Chow groups of certain bicyclic coverings are trivial without tensoring.

Results apply to topologically contractible smooth affine complex varieties.

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 $\mathbb{Q}$.