isUnramified_iff_mult_le — Mathlib

English

Unramified over k is equivalent to the comparison of ramification multiplicities: mult w ≤ mult (w.comap (algebraMap k K)).

Русский

Неразмороженность над k эквивалентна сравнению мультипликаторов: mult w ≤ mult (w.comap (algebraMap k K)).

LaTeX

$$$\\operatorname{IsUnramified} \\,k\,w \\iff \\operatorname{mult} w \\le \\operatorname{mult} (w.\\mathrm{comap}(\\operatorname{algebraMap}\\;k\\;K))$$$

Lean4

theorem isUnramified_iff_mult_le : IsUnramified k w ↔ mult w ≤ mult (w.comap (algebraMap k K)) :=
  by
  rw [IsUnramified, le_antisymm_iff, and_iff_right]
  exact mult_comap_le _ _

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