isLocallyFraction — Mathlib

English

The structure sheaf is defined by local fractions; IsLocallyFraction is the predicate that a dependent function assigns to fractions, respected by restriction and compatible with algebraic structure.

Русский

Структура оболочки задаётся локальными дробями; IsLocallyFraction — предикат, для которого функция признаков принадлежит дробям, сохраняется при ограничении и совместима с алгебраической структурой.

LaTeX

$$$$\text{IsLocallyFraction}\ 𝒜\; f = \text{something like the fraction predicate per prime}$$$$

Lean4

/-- We will define the structure sheaf as the subsheaf of all dependent functions in
`Π x : U, HomogeneousLocalization 𝒜 x` consisting of those functions which can locally be expressed
as a ratio of `A` of same grading. -/
def isLocallyFraction : LocalPredicate fun x : ProjectiveSpectrum.top 𝒜 => at x :=
  (isFractionPrelocal 𝒜).sheafify

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