Strong approximation and a conjecture of Harpaz and Wittenberg

In recent work Harpaz and Wittenberg established a general fibration theorem for the existence of rational points, conditional on a conjecture on locally split values of polynomials. In this talk we report on joint work with Tim Browning, which establishes a special case of their conjecture. We achieve this in proving strong approximation off a non-empty finite set of places for some varieties which are defined using norm forms.