\'Etale Brauer-Manin obstruction for Weil restrictions

TL;DR

This paper demonstrates that the étale Brauer-Manin obstruction remains equivalent across Weil restrictions of any quasi-projective algebraic variety over a number field, highlighting a fundamental invariance property.

Contribution

It establishes the invariance of the étale Brauer-Manin obstruction under Weil restrictions for quasi-projective varieties over number fields.

Findings

Étale Brauer-Manin obstruction is invariant under Weil restrictions.

The result applies to arbitrary quasi-projective algebraic varieties.

Provides a unifying perspective on obstructions in arithmetic geometry.

Abstract

The \'etale Brauer\textendash Manin obstruction is equivalent to each other among Weil restrictions of an arbitrarily given quasi-projective algebraic variety defined over a number field.