Commutators in $\mathrm{SL}_2$ and Markoff surfaces I
Number Theory
2022-01-20 v2 Group Theory
Abstract
We show that the commutator equation over satisfies a profinite local to global principle, while it can fail with infinitely many exceptions for . The source of the failure is a reciprocity obstruction to the Hasse Principle for cubic Markoff surfaces.
Cite
@article{arxiv.2110.11030,
title = {Commutators in $\mathrm{SL}_2$ and Markoff surfaces I},
author = {Amit Ghosh and Chen Meiri and Peter Sarnak},
journal= {arXiv preprint arXiv:2110.11030},
year = {2022}
}
Comments
Minor edits