Le principe de Hasse pour les intersections de deux quadriques dans $\mathbb{P}^7$

Abstract

We prove the Hasse principle for a smooth proper model of a geometrically integral non-conical intersection of two quadrics in the projective space of dimension 7 over a number field. This result generalizes the result of Heath-Brown who established the statement in the smooth case. Our argument is built upon the ideas of Colliot-Th\'el\`ene and the fibration method for zero-cycles in the form of Harpaz-Wittenberg.