Brauer-Manin obstruction for zero-cycles on certain varieties

TL;DR

This paper explores how the Brauer-Manin obstruction can prevent the existence of zero-cycles of certain degrees on specific varieties, providing examples and insights into this phenomenon.

Contribution

It demonstrates that the Brauer-Manin obstruction can explain the absence of zero-cycles of given degrees on certain varieties, with new examples illustrating this obstruction.

Findings

Brauer-Manin obstruction can prevent zero-cycles of specific degrees

Examples show the obstruction's role in zero-cycle non-existence

Insights into the relationship between local zero-cycles and global obstructions

Abstract

We investigate the question of whether the existence of a family of local zero-cycles of degree $d$ orthogonal to the Brauer group implies the non-emptiness of the Brauer-Manin set for certain varieties. We provide various examples of Brauer-Manin obstruction to the existence of zero-cycles of appropriate degrees.