On the obstruction to the Hasse principle for multinorm equations

TL;DR

This paper studies the failures of the Hasse principle for multinorm equations over global fields, providing explicit formulas for obstructions and extending previous results in the area.

Contribution

It generalizes prior work to give explicit, computable formulas for obstructions to the Hasse principle and weak approximation for multinorm equations.

Findings

Derived explicit formulas for obstructions to the Hasse principle.

Extended previous results to broader classes of multinorm equations.

Demonstrated the applicability of the formulas through examples.

Abstract

We investigate local-global principles for multinorm equations over a global field. To this extent, we generalize work of Drakokhrust and Platonov to provide explicit and computable formulae for the obstructions to the Hasse principle and weak approximation for multinorm equations. We illustrate the scope of this technique by extending results of Bayer-Fluckiger--Lee--Parimala, Demarche--Wei and Pollio.