The Chevalley-Warning Theorem states that if a finite field has characteristic p, and a collection of polynomials in more variables than the sum of their degrees is given over that field, then the number of common solutions to those polynomials is divisible by p, which in particular forces a nontrivial solution to exist whenever the all-zero solution does. Named for Claude Chevalley and Ewald Warning, it is a foundational result in the study of polynomial equations over finite fields, with the existence of nontrivial solutions originally conjectured by Emil Artin.
Facts
StatementFor a system of polynomials over a finite field with total degree less than the number of variables, the number of common solutions is divisible by the characteristic p of the field. 1 Classification
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Source Chevalley-Warning theorem (Wikipedia)
Proved By
Source Chevalley-Warning theorem (Wikipedia)
Sources
1. Chevalley-Warning theorem (Wikipedia)
Lead section
It was proved by Ewald Warning (1935) and a slightly weaker form of the theorem, known as Chevalley's theorem, was proved by Chevalley (1935).
Historical Context
It was proved by Ewald Warning (1935) and a slightly weaker form of the theorem, known as Chevalley's theorem, was proved by Chevalley (1935).
- In Branch: Number Theory, Lead sentence
Proved By: Claude Chevalley, Lead sentence, attribution
was proved by Chevalley (1935)
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