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ClassFieldTheory

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A Lean 4 formalization of local and global class field theory. It proves local reciprocity and the local existence theorem; global Artin reciprocity and the finite and infinite abelian class-field correspondences; conductor theory, norm limitation, and principalization in the Hilbert class field. It also proves Hasse–Arf, local and global Kronecker–Weber, the Hilbert-symbol product formula, power-residue reciprocity, and derives Gauss's quadratic reciprocity.

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Formalized results

  • Local reciprocity and the local existence theorem.
  • Global Artin reciprocity and finite and infinite abelian class-field correspondences.
  • Conductor theory, norm limitation, and principalization in the Hilbert class field.
  • Hasse–Arf and the local and global Kronecker–Weber theorems.
  • The Hilbert-symbol product formula, power-residue reciprocity, and Gauss's quadratic reciprocity.