Abstract: In recent joint work with Sam Streeter and Rosa Winter, we show that weak weak approximation holds for Del Pezzo surfaces of degree 2 (over a number field) with a rational point not lying on the ramification curve or on the intersection of 4 exceptional curves. To prove this, we use two geometric “procedures” to produce rational points on the surface. The points obtained by a certain iteration of these two procedures are parametrized by a rational higher-dimensional cover of the surface, and we deduce our result by proving the arithmetic surjectivity of the morphism defining the cover.

Zoom id: https://arizona.zoom.us/j/83621467612