# The Stacks Project

## Tag 0AAR

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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