Brauer-Manin obstruction for integral points on Markoff-type cubic surfaces
Number Theory
2023-12-18 v4 Algebraic Geometry
Abstract
Following [GS22], [LM20] and [CWX20], we study the Brauer-Manin obstruction for integral points on similar Markoff-type cubic surfaces. In particular, we construct a family of counterexamples to strong approximation which can be explained by the Brauer-Manin obstruction with some counting results of similar nature to those in [LM20] and [CWX20]. We also give some counterexamples to the integral Hasse principle which cannot be explained by the (algebraic) Brauer-Manin obstruction.
Keywords
Cite
@article{arxiv.2202.07142,
title = {Brauer-Manin obstruction for integral points on Markoff-type cubic surfaces},
author = {Quang-Duc Dao},
journal= {arXiv preprint arXiv:2202.07142},
year = {2023}
}
Comments
34 pages; this version comes from the accepted manuscript of the article published in the Journal of Number Theory