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Additive combinatorics and rational points: an update

Alexei Skorobogatov
Imperial

Heilbronn

Organisers: Tim Dokchitser, Daniel Loughran

ABSTRACT
The generalised Hardy-Littlewood conjecture proved recently by Green, Tao and Ziegler has far reaching consequences for rational points on algebraic varieties over Q. It can be used instead of Schinzel's Hypothesis (H) in the case of linear polynomials. This makes unconditional some of the results that previously depended on Schinzel's Hypothesis, giving a shorter proof and a somewhat longer list of applications than a recent joint paper with Browning and Matthiesen. This is a joint work with Y. Harpaz and O. Wittenberg.