Gabber's presentation lemma for finite fields

TL;DR

This paper proves Gabber's presentation lemma for finite fields by reducing the general case to a special case in the affine plane, utilizing ideas from Poonen's Bertini theorem proof.

Contribution

It provides a new proof of Gabber's presentation lemma over finite fields, extending the understanding of smooth varieties in algebraic geometry.

Findings

Proof of Gabber's presentation lemma for finite fields

Reduction of the general case to the affine plane case

Application of Poonen's Bertini theorem ideas

Abstract

We give a proof of Gabber's presentation lemma for finite fields. We use ideas from Poonen's proof of Bertini's theorem to prove this lemma in the special case of open subsets of the affine plane. We then reduce the case of general smooth varieties to this special case.