Hasse norm principle for extensions of prime squared degree

TL;DR

This paper establishes an equivalent condition for the Hasse norm principle in prime squared degree extensions over global fields, generalizing previous results and providing a new criterion for its validity.

Contribution

It introduces a new equivalent condition for the Hasse norm principle in prime squared degree extensions, extending prior work by Drakokhrust and Platonov.

Findings

The Hasse norm principle holds under the new equivalent condition.

The theorem recovers and generalizes previous results.

Provides a criterion applicable to a broad class of extensions.

Abstract

We give an equivalent condition for the validity of the Hasse norm principle for finite separable extensions of prime squared degree of global fields. Our theorem recovers the result of Drakokhrust--Platonov, which claims that the Hasse norm principle holds for adequate extensions of prime squared degree.