Brauer-Manin obstruction for Markoff surfaces

J. -L. Colliot-Thélène, Dasheng Wei, Fei Xu

Published 2018-08-05Version 1

Ghosh and Sarnak have studied integral points on surfaces defined by an equation $x^2+y^2+z^2-xyz= m$ over the integers. For these affine surfaces, we systematically study the Brauer group and the Brauer-Manin obstruction to strong approximation and the integral Hasse principle. We produce surfaces for which integral points are Zariski dense but are not dense in the integral Brauer-Manin set.