Commutators in $SL_2$ and Markoff surfaces I

Amit Ghosh; Chen Meiri; Peter Sarnak

doi:10.53733/198

Commutators in $SL_2$ and Markoff surfaces I

Authors

Amit Ghosh Oklahoma State University
Chen Meiri Technion - Israel Institute of Technology
Peter Sarnak Institute for Advanced Study and Princeton University

DOI:

https://doi.org/10.53733/198

Abstract

We show that the commutator equation over $SL_2\Z$ satisfies a profinite local to global principle, while it can fail with infinitely many exceptions for $SL_2(\Z[\frac{1}{p}])$. The source of the failure is a reciprocity obstruction to the Hasse Principle for cubic Markoff surfaces.

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Published

18-01-2022

How to Cite

Ghosh, A., Meiri, C., & Sarnak, P. (2022). Commutators in $SL_2$ and Markoff surfaces I. New Zealand Journal of Mathematics, 52, 773–819. https://doi.org/10.53733/198