Local–global principles for semi‐integral points on Markoff orbifold pairs

Abstract We study local–global principles for semi‐integral points on orbifold pairs of Markoff type. In particular, we analyse when these orbifold pairs satisfy weak weak approximation, weak approximation and strong approximation off a finite set of places. We show that Markoff orbifold pairs satisfy the semi‐integral Hasse principle and we measure how often such orbifold pairs have strict semi‐integral points but the corresponding Markoff surface lacks integral points.