Hasse principle for the Chow groups on quadric fibrations

TL;DR

This paper establishes a sufficient condition ensuring the injectivity of the global-to-local map for the relative Chow group of zero-cycles on certain quadric fibrations over number fields, advancing understanding of local-global principles.

Contribution

It provides new criteria for the injectivity of the global-to-local map in the context of quadric fibrations of dimension 2 or 3 over number fields.

Findings

Identifies a sufficient condition for injectivity of the global-to-local map.

Applies to quadric fibrations of dimension 2 or 3.

Enhances understanding of the Hasse principle for Chow groups.

Abstract

We give a sufficient condition for the injectivity of the global-to-local map of the relative Chow group of zero-cycles on a quadric fibration of dimension 2 or 3 defined over a number field.