algebraMap_iterateFrobenius — Mathlib

English

There exists an equality relating the base-algebra map and the iterated Frobenius, when the exponent bounds hold; specifically algebraMap_KL(iterateFrobenius...) equals a^{p^{n}}.

Русский

Существуют равенства, связывающие образ алгебраMap и итерацию Фробениуса: algebraMap_KL(iterateFrobenius(...)) = a^{p^{n}}.

LaTeX

$$$\operatorname{algebraMap} K L\, (\operatorname{iterateFrobenius} K L p \ hn a) = a^{p^{n}}$$$

Lean4

/-- Action of `iterateFrobenius` on the top field. -/
theorem algebraMap_iterateFrobenius {n : ℕ} (hn : exponent K L ≤ n) (a : L) :
    algebraMap K L (iterateFrobenius K L p hn a) = a ^ p ^ n :=
  algebraMap_iterateFrobeniusAux K p hn a

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