We show that the commutator equation over SL2(Z) satisfies a profinite local to global principle, while it can fail with infinitely many exceptions for SL2(Z[p1 ]). The source of the failure is a reciprocity obstruction to the Hasse Principle for cubic Markoff surfaces.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology
- Applied Mathematics