@article{Ghosh_Meiri_Sarnak_2022, title={Commutators in $SL_2$ and Markoff surfaces I}, volume={52}, url={https://nzjmath.org/index.php/NZJMATH/article/view/198}, DOI={10.53733/198}, abstractNote={<p>We show that the commutator equation over $SL_2\Z$ satisfies a profinite local to global principle, while it can fail with infinitely many<span class="Apple-converted-space">  </span>exceptions for $SL_2(\Z[\frac{1}{p}])$. The source of the failure is a reciprocity obstruction<span class="Apple-converted-space"> </span>to the Hasse Principle for cubic Markoff surfaces.</p>}, journal={New Zealand Journal of Mathematics}, author={Ghosh, Amit and Meiri, Chen and Sarnak, Peter}, year={2022}, month={Jan.}, pages={773–819} }