Brauer-Manin obstruction for integral points on Markoff-type cubic surfaces
arXiv:2202.07142 · doi:10.1016/j.jnt.2023.07.007
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.
34 pages; this version comes from the accepted manuscript of the article published in the Journal of Number Theory