Let X be a smooth irreducible curve over a separably closed field k. Then is there smooth projective curve $\bar X$ over $k$ which admits an open immersion $X\hookrightarrow \bar X$?
This question comes from a book $\it{Etale\ Cohomology\ theory}$(Lei Fu) proposition 7.2.10. In the book, there's no definition for the word "curve", so I assume it means a scheme of finite type over a field $k$ with dimension 1.