COMMUTATORS IN SL2 AND MARKOFF SURFACES I

Amit Ghosh; Chen Meiri; Peter Sarnak

doi:10.53733/198

COMMUTATORS IN SL₂ AND MARKOFF SURFACES I

Amit Ghosh, Chen Meiri, Peter Sarnak

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	773-819
Number of pages	47
Journal	New Zealand Journal of Mathematics
Volume	52
DOIs	https://doi.org/10.53733/198
State	Published - 2021

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

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10.53733/198

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title = "COMMUTATORS IN SL2 AND MARKOFF SURFACES I",

abstract = "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.",

author = "Amit Ghosh and Chen Meiri and Peter Sarnak",

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year = "2021",

doi = "10.53733/198",

language = "English (US)",

volume = "52",

pages = "773--819",

journal = "New Zealand Journal of Mathematics",

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T1 - COMMUTATORS IN SL2 AND MARKOFF SURFACES I

AU - Ghosh, Amit

AU - Meiri, Chen

AU - Sarnak, Peter

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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DO - 10.53733/198

M3 - Article

AN - SCOPUS:85124102622

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VL - 52

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EP - 819

JO - New Zealand Journal of Mathematics

JF - New Zealand Journal of Mathematics

ER -

COMMUTATORS IN SL₂ AND MARKOFF SURFACES I

Abstract

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