Integral points on generalised affine Châtelet surfaces (Q2305862)

The paper under review proves, under Schinzel's Hypothesis, that the Brauer-Manin obstruction is the only obstruction to the existence of integral points on any of a large class of Châtelet surfaces. The proof proceeds by a careful set of constructions of elements of the Brauer group of the surface, expressed elegantly in terms of the defining polynomial. The author also proves an auxiliary result, of independent interest, on the existence of integral points on affine conics. Specifically, they prove that a quadratic norm form equation \(N(x,y)=C\) has integral points if and only if it has rational points, provided that the prime factorization of \(C\) takes a certain form with respect to the field associated to \(N\).