Elementary fibrations over finite fields

I. Panin

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: In 1973 M. Artin introduced a notion of an elementary fibration. It is a very useful tool for various applications. In this paper we give a detailed proof of existences of an elementary fibration for smooth affine varieties over a finite field. A short version of that has been published in a paper of mine (Izvestia RAS, 2019). To give the detailed proof we use our extension of Poonen's form of Bertini type theorems over a finite field.

Key words and phrases: Bertini type theorems, elementary fibrations, finite fields.

UDC: 512.74

Received: 30.11.2025

Language: English