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  "body": "\n## Summary\n\nA finite morphism $X \\to Y$ of schemes is affine over $Y$.\nOver each affine piece $\\operatorname{Spec} B$ of $Y$, it comes from a $B$-algebra that is a finitely generated $B$-module.\nIt is the scheme version of a [[finite morphism of rings|1NBACAEC2V]].\nFinite morphisms have finite fibers and are closed maps; branched covers of curves are typical examples.\n\n## Explanations\n\n### L1 human\n\nA finite morphism is like a map where each point has finitely many points above it, and nothing escapes to infinity.\nThe map $t \\mapsto t^2$ from the complex line to the complex line is finite: above each nonzero point there are two points, and above $0$ there is one.\nThe inclusion of the punctured line into the line is not finite, because points near the removed origin escape.\nClosed immersions are finite as well.\n",
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