Hasse norm principle for extensions of prime squared degree

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.

arXiv comment38 pages, some notation and numbering of theorems are changed. Text overlap with arXiv:2504.19453