Integral points on generalised affine Ch\^atelet surfaces

TL;DR

This paper demonstrates, under Schinzel's hypothesis, that the Brauer--Manin obstruction is the sole barrier to the integral Hasse principle on generalized affine Châtelet surfaces, linking arithmetic obstructions to geometric properties.

Contribution

It establishes a conditional result identifying the Brauer--Manin obstruction as the only obstacle to the integral Hasse principle for these surfaces.

Findings

Conditional proof based on Schinzel's hypothesis

Identification of Brauer--Manin obstruction as the only barrier

Advances understanding of integral points on Châtelet surfaces

Abstract

We show, conditionally on Schinzel's hypothesis, that the only obstruction to the integral Hasse principle for generalised affine Ch\^{a}telet surfaces is the Brauer--Manin one.