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Measured Foliations and Hilbert 12th Problem

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.

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Correspondence to Igor V. Nikolaev.

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Nikolaev, I.V. Measured Foliations and Hilbert 12th Problem. Acta Math Vietnam (2022). https://doi.org/10.1007/s40306-022-00479-w

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  • DOI: https://doi.org/10.1007/s40306-022-00479-w

Keywords

  • Class field theory
  • Measured foliations

Mathematics Subject Classification (2010)

  • Primary 11G45
  • Secondary 57R30