Brauer-Manin obstruction for Markoff-type cubic surfaces

Quang-Duc Dao

Published 2022-02-15Version 1

Following the works by Ghosh and Sarnak; Loughran and Mitankin; Colliot-Th\'el\`ene, Wei, and Xu, we study the local-global principle and Brauer--Manin obstruction for integral points on similar Markoff-type cubic surfaces. Furthermore, we construct a family of counterexamples to the integral Hasse principle which can be explained by the Brauer--Manin obstruction with a greater frequency, compared to the results given by Loughran and Mitankin; Colliot-Th\'el\`ene, Wei, and Xu.