Absolute reconstruction of number fields from the Deligne-Ribet monoids
Abstract
Following Cornelissen, Li, Marcolli, and Smit, this short paper proves that the field structure of a number field K can be reconstructed from the pair (DRK, IK) of the Deligne-Ribet monoid DRK and the submonoid IK of DRK, when K is the rational number field, or an imaginary quadratic field. The general-case reconstruction is also discussed, which is more abstract than the case of rational and imaginary quadratic fields.
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