English

Integral points on affine quadric surfaces

Algebraic Geometry 2022-10-10 v1 Number Theory

Abstract

It is well-known that the Hasse principle holds for quadric hypersurfaces. The Hasse principle fails for integral points on smooth quadric hypersurfaces of dimension 2 but the failure can be completely explained by the Brauer-Manin obstruction. We investigate how often the family of quadric hypersurfaces ax2+by2+cz2=nax^2 + by^2 +cz^2 = n has a Brauer-Manin obstruction. We improve previous bounds of Mitankin.

Keywords

Cite

@article{arxiv.2010.11763,
  title  = {Integral points on affine quadric surfaces},
  author = {Tim Santens},
  journal= {arXiv preprint arXiv:2010.11763},
  year   = {2022}
}
R2 v1 2026-06-23T19:33:32.307Z