Brauer groups of certain affine cubic surfaces
Algebraic Geometry
2025-10-30 v2 Number Theory
Abstract
We study the Brauer groups of affine surfaces that are complements of singular hyperplane sections of smooth cubic surfaces over a field of characteristic . We determine the Brauer group over the algebraic closure as a Galois module for all the possible singular hyperplane sections. For the case when the hyperplane section is geometrically the union of three lines, we give explicit examples where transcendental elements of order and exist over . We end with an application on the integral Brauer-Manin obstruction to the integral Hasse principle.
Cite
@article{arxiv.2509.16042,
title = {Brauer groups of certain affine cubic surfaces},
author = {Abdulmuhsin Alfaraj},
journal= {arXiv preprint arXiv:2509.16042},
year = {2025}
}