Commutators in $SL_2$ and Markoff surfaces I

Amit Ghosh, Chen Meiri, Peter Sarnak

Type: Article

Publication Date: 2022-01-18

Citations: 3

DOI: https://doi.org/10.53733/198

Abstract

We show that the commutator equation over $\mathrm{SL}_2(\mathbb{Z})$ satisfies a profinite local to global principle, while it can fail with infinitely many exceptions for $ \mathrm{SL}_2(\mathbb{Z}[\frac{1}{p}])$. The source of the failure is a reciprocity obstruction to the Hasse Principle for cubic Markoff surfaces.

Locations

New Zealand journal of mathematics - View - PDF
arXiv (Cornell University) - View - PDF
SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University) - View - PDF
DataCite API - View
New Zealand journal of mathematics - View - PDF
arXiv (Cornell University) - View - PDF
SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University) - View - PDF
DataCite API - View
New Zealand journal of mathematics - View - PDF
arXiv (Cornell University) - View - PDF
SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University) - View - PDF
DataCite API - View

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Action	Title	Year	Authors
+	Finite approximation and commutators in free groups	2004	Anatole Khélif
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