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Does anyone know of generalizations on what Mumford (Red Book) calls "uniformizing parameters"? For example, given a regular quasi-projective scheme over a finite field $\mathbb{F}$, find is there an etale morphism into affine space over $\mathbb{F}$. \mathbb{F}$?.

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Does anyone know of generalizations on what Mumford (Red Book) calls "uniformizing parameters"? For example, given a regular projective quasi-projective scheme over a finite field $\mathbb{F}$, find an etale morphism into affine space over $\mathbb{F}$. This sounds like a folk conjecture...

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When does a projective morphism give an etale morphism (into affine space)? (Finite field) (Gabber's normalization)normalization)

Does anyone know of generalizations on what Mumford (Red Book) calls "uniformizing parameters"? For example, given a regular projective scheme over a finite field $\mathbb{F}$, find an etale morphism into affine space over $\mathbb{F}$. This sounds like a folk conjecture, eg what might be called "Gabber's version of Noether normalization"conjecture...Perhaps one can achieve such a result using his recent uniformization theorems?

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