Word.ws English Dictionary

Ax-Grothendieck theorem

Ax-Grothendieck theorem proper noun: 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.

Proper noun

the Ax-Grothendieck theorem

  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.

Origin of Ax-Grothendieck theorem

Proved independently by James Ax and Alexander Grothendieck.

Questions about Ax-Grothendieck theorem

What does Ax-Grothendieck theorem mean?
Ax-Grothendieck theorem means 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.
What part of speech is Ax-Grothendieck theorem?
Ax-Grothendieck theorem is a proper noun.

Words near Ax-Grothendieck theorem in the dictionary

  1. Awyoung
  2. ax
  3. ax head
  4. ax heads
  5. ax to grind
  6. Ax-Grothendieck theorem
  7. Ax-Kochen theorem
  8. axal
  9. axanthic
  10. axanthine
  11. axanthism

Source and license

Adapted from Wiktionary: Ax-Grothendieck theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “Ax-Grothendieck theorem.” Word.ws, https://word.ws/ax-grothendieck_theorem. Based on Wiktionary, CC BY-SA 4.0.