How to use finite fields for problems concerning infinite fields

TL;DR

This paper explains how finite fields can be used to prove theorems about infinite fields through reduction mod p, and presents a variant of P. Smith's fixed point theorem applicable in any characteristic.

Contribution

It introduces a method to transfer results from finite to infinite fields and extends fixed point theorems to broader settings.

Findings

Finite fields can be used to prove theorems on infinite fields via reduction mod p.

A variant of P. Smith's fixed point theorem is developed for any characteristic.

The paper provides expository insights and new theoretical extensions.

Abstract

The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.