Ax-Grothendieck theorem
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English
Etymology
Proved independently by James Ax and Alexander Grothendieck.
Proper noun
the Ax-Grothendieck theorem
- (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.