Chow groups of one-dimensional noetherian domains

TL;DR

This paper explores the relationships between ideal classes, divisors, Picard, and Chow groups in one-dimensional noetherian domains, providing methods for computing Chow groups of orders in global fields and demonstrating the existence of number fields with trivial Chow groups.

Contribution

It introduces a method to compute Chow groups of orders in global fields and proves the existence of infinitely many number fields with trivial Chow groups.

Findings

Method for computing Chow groups of orders in global fields

Existence of infinitely many number fields with trivial Chow groups

Connections established between ideal classes, divisors, Picard, and Chow groups

Abstract

We discuss various connections between ideal classes, divisors, Picard and Chow groups of one-dimensional noetherian domains. As a result of these, we give a method to compute Chow groups of orders in global fields and show that there are infinitely many number fields which contain orders with trivial Chow groups.