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Measured foliations and Hilbert 12th problem

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arxiv 0804.0057 v9 pith:GMBSOBFR submitted 2008-04-01 math.NT math.OA

Igor Nikolaev This is my paper · ORCID
classification math.NTmath.OA
keywords foliationsmeasuredrealabelianconjectureconjecturedcurvesextensions
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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.

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  1. Addendum to "Measured foliations and Hilbert 12th problem"

    math.NT 2025-05 reject novelty 4.0 of 10

    The paper asserts that ring class fields of real quadratic fields Q(√p) for primes p ≡ 3 mod 4 are contained in coefficient fields of certain modular forms, but the proof is incomplete and contradicts its own p=7 example.

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