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Tag 0AAR

Chapter 102: Exercises > Section 102.54: Schemes, Final Exam, Spring 2014

Exercise 102.54.5. Let $k$ be a field. Let $X$ be a projective variety over $k$. Show there exists an affine variety $U$ over $k$ and a surjective morphism of varieties $U \to X$.

    The code snippet corresponding to this tag is a part of the file exercises.tex and is located in lines 5664–5669 (see updates for more information).

    \begin{exercise}
    \label{exercise-surjective-map-affine-variety-projective-variety}
    Let $k$ be a field. Let $X$ be a projective variety over $k$.
    Show there exists an affine variety $U$ over $k$ and a surjective
    morphism of varieties $U \to X$.
    \end{exercise}

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