Schinzel's Hypothesis with probability 1 and rational points on varieties in families (in two parts)

Alexei Skorobogatov (Imperial College London/FRIAS University of Freiburg)

Sep 20. 2021, 16:30 — 17:30

We prove that Schinzel's Hypothesis (H) holds for 100% of polynomials of any fixed degree. The first talk by Efthymios Sofos will discuss the proof of this result, which uses a truncated version of the von Mangoldt function and takes advantage of cancellation properties of the Moebius function. In the second talk, Alexei Skorobogatov 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 and diagonal conic bundles of any fixed degree over the projective line.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Arithmetic Statistics and Local-Global Principles (Workshop)
Tim Browning (ISTA, Klosterneuburg)
Daniel Loughran (U Bath)
Rachel Newton (KCL, London)