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  "body": "\n## Summary\n\nA proper morphism of schemes is a morphism that is separated, of finite type and universally closed.\nIt is the algebraic analogue of a proper map of topological spaces, and of a compact space when the target is a point.\nMany finiteness results, such as the finiteness of cohomology of coherent sheaves and the existence of the Stein factorization, hold for proper morphisms.\n\n## Explanations\n\n### L1 human\n\nA proper morphism is a family of spaces in which no fibre has points \"missing at infinity\".\nProjective space over a field is proper over that field, while the affine line is not.\nThe affine line misses the point at infinity: a point moving off to infinity has no limit in it.\nProperness rules out this kind of escape, and so it plays the role of compactness in algebraic geometry.\n",
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