Arithmetic Groups

Commutators in SL_2 and Markoff Surfaces

We discuss a local to global profinite principle for being a commutator in some arithmetic groups. Specifically we show that $SL_2(Z)$ satisfies such a principle, while it can fail with infinitely many exceptions for $SL_2(Z[1/p])$. The source of the failure is a reciprocity obstruction to the integral Hasse Principle for cubic Markoff surfaces. Joint work with Amit Ghosh and Peter Sarnak.

Date & Time

December 15, 2021 | 11:00am – 12:15pm

Location

Simonyi 101 and Remote Access

Affiliation

Technion

Event Series

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