ChevalleyWarning
The Chevalley–Warning theorem, sometimes referred to simply as Chevalley–Warning, is a result in finite field theory and algebraic geometry that concerns the number of common solutions to polynomial equations over finite fields. It provides a divisibility property for the number of solutions under a constraint on the total degrees of the polynomials.
Let F be a finite field with q elements, where q = p^r and p is its characteristic.
The theorem emerged from work by Claude Chevalley and Émile Warning in the mid-1930s and is named
Applications of the result appear in number theory, combinatorics, and the study of polynomial mappings over