Ax-Grothendieck theorem

English

Etymology

Proved independently by James Ax and Alexander Grothendieck.

Proper noun

the Ax-Grothendieck theorem

1. (mathematics) A result about injectivity and surjectivity of polynomials, often given as this special case: If P is an injective polynomial function from an n-dimensional complex vector space to itself then P is bijective. The full theorem generalizes to any algebraic variety over an algebraically closed field.