Measured foliations and Hilbert 12th problem

TL;DR

This paper proves Manin's conjecture that maximal abelian extensions of real quadratic fields are generated by pseudo-lattices with real multiplication, using measured foliations on modular curves.

Contribution

It provides a proof of Manin's conjecture by connecting measured foliations with class field theory for real quadratic fields.

Findings

Maximal abelian extensions are generated by pseudo-lattices with real multiplication.

Measured foliations on modular curves are instrumental in the proof.

Confirms conjectured relationship between measured foliations and number field extensions.

Abstract

Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are generated by the pseudo-lattices with real multiplication. We prove this conjecture using theory of measured foliations on the modular curves.