A Note On a Theorem of Heath-Brown and Skorobogatov

TL;DR

This paper extends a theorem by Heath-Brown and Skorobogatov to demonstrate that specific algebraic varieties over number fields adhere to the Hasse principle and weak approximation when no Brauer-Manin obstruction exists.

Contribution

The paper generalizes a previous result to a broader class of varieties, establishing conditions for the Hasse principle and weak approximation.

Findings

Varieties satisfy the Hasse principle under certain conditions.

Weak approximation holds for the considered class of varieties.

No Brauer-Manin obstruction implies the validity of these properties.

Abstract

We generalise a result of Heath-Brown and Skorobogatov to show that a certain class of varieties over a number field $k$ satisfies Weak Approximation and the Hasse Principle, provided there is no Brauer-Manin obstruction.