On the Hasse principle for certain quartic hypersurfaces

Source abstract

We prove that there are infinitely many non-isomorphic quartic curves which are counter-examples to the Hasse principle explained by the Brauer-Manin obstruction. Further, these quartic curves have no points defined over number fields of odd degree. As a consequence, we show that there are infinitely many quartic hypersurfaces of arbitrary dimension violating the Hasse principle.