Cubic surfaces failing the integral Hasse principle

authored by

Julian Lyczak, Vladimir Mitankin, H. Uppal

Abstract

We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this setting. We then count in three natural ways how such counterexamples are distributed across the family of affine diagonal cubic surfaces and how often such surfaces satisfy integral strong approximation off $\infty$.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Preprint

Publication date

16.11.2023

Publication status

Published