Cubic surfaces failing the integral Hasse principle

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE 2026 Open access

Read full text
Authors: Julian Lyczak, Vladimir Mitankin, H. Uppal
DOI: 10.2422/2036-2145.202511_016
Cited by: 0

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 ∞.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Mathematical Dynamics and Fractals Advanced Combinatorial Mathematics

Publication details

Journal / source
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
Publisher
Scuola Normale Superiore - Edizioni della Normale
Pages
36–36
Publication date
26 June 2026
Language
EN