"Ax-Grothendieck theorem" meaning in English

{
  "etymology_text": "Proved independently by James Ax and Alexander Grothendieck.",
  "forms": [
    {
      "form": "the Ax-Grothendieck theorem",
      "tags": [
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  "lang_code": "en",
  "pos": "name",
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      "glosses": [
        "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."
      ],
      "id": "en-Ax-Grothendieck_theorem-en-name-v-xzP-AZ",
      "links": [
        [
          "mathematics",
          "mathematics"
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        [
          "injectivity",
          "injectivity"
        ],
        [
          "surjectivity",
          "surjectivity"
        ],
        [
          "polynomial",
          "polynomial"
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          "complex",
          "complex"
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          "vector space",
          "vector space"
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        [
          "bijective",
          "bijective"
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      ],
      "raw_glosses": [
        "(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."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Ax-Grothendieck theorem"
      ]
    }
  ],
  "word": "Ax-Grothendieck theorem"
}

{
  "etymology_text": "Proved independently by James Ax and Alexander Grothendieck.",
  "forms": [
    {
      "form": "the Ax-Grothendieck theorem",
      "tags": [
        "canonical"
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        "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."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
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          "injectivity",
          "injectivity"
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          "surjectivity",
          "surjectivity"
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          "polynomial",
          "polynomial"
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        "(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."
      ],
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        "mathematics",
        "sciences"
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  ],
  "word": "Ax-Grothendieck theorem"
}