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arXiv · 2202.07142

Brauer-Manin obstruction for integral points on Markoff-type cubic surfaces

Quang-Duc Dao
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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.

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BibTeXRIS

Quang-Duc Dao. 2022-02-15. Brauer-Manin obstruction for integral points on Markoff-type cubic surfaces. https://doi.org/10.1016/j.jnt.2023.07.007

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