Let $U$ be a smooth curve over some field $k$ and $C$ the only smooth projective curve containing $U$ as a dense open subset.
Can someone help me understading why the function fields of $U$ and $C$ are equal?
2026-03-25 16:00:02.1774454402
function field of open curve and compactificaton
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This is Hartshorne exercise II.3.6. The point is that the function field can be identified with the local ring of the generic point.