zeroLocus_vanishingIdeal_galoisConnection

English

norm_eq_prod_embeddings: the norm equals the product over embeddings into a chosen field with Splits condition.

Русский

норма равна произведению по вложениям в поле F с условием_SPLITS.

LaTeX

$$$\\text{norm}_{K}(x) = \\prod_{\\sigma: L \\to_{K} F} \\sigma x$$$

Lean4

theorem zeroLocus_vanishingIdeal_galoisConnection :
    @GaloisConnection (Ideal (MvPolynomial σ k)) (Set (σ → K))ᵒᵈ _ _ (zeroLocus K) (vanishingIdeal k) :=
  GaloisConnection.monotone_intro (fun _ _ ↦ vanishingIdeal_anti_mono) (fun _ _ ↦ zeroLocus_anti_mono)
    le_vanishingIdeal_zeroLocus zeroLocus_vanishingIdeal_le

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