English Explanatory Dictionary

Ax-Grothendieck theorem

English dictionary entry

Meanings

name
  1. 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.

Word forms

Ax-Grothendieck theorem the Ax-Grothendieck theorem

Etymology

Proved independently by James Ax and Alexander Grothendieck.

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