Extensions of Poonen's theorems

I. Panin

St. Petersburg Branch of V. A. Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia

Abstract: We prove some extensions of Poonen's form of Bertini type theorems over a finite field. These extensions are stated and proved in section 2. First applications are given in section 3. Further applications will be given in a next paper.

Key words and phrases: finite fields, Bertini type theorems, Poonen's theorems.

UDC: 512.74

Received: 30.11.2025

Language: English