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Schinzel's Hypothesis with probability 1 and rational points on varieties in families

Alexei Skorobogatov

Freitag, 26. November 2021 10:30Uhr

In a joint work with Efthymios Sofos we prove that Schinzel's Hypothesis (H) holds for 100% of polynomials of any fixed degree. I will pass in silence the proof of this analytic result, but will explain how to deduce from this that among varieties in specific families over Q, a positive proportion have rational points. The main examples are varieties given by generalised Châtelet equations (a norm form equals a polynomial) and diagonal conic bundles of any fixed degree over the projective line.