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  "body": "\n## Summary\n\nA scheme is a [[locally ringed space|B7FPT8JTXR]] that looks, near each point, like an [[affine scheme|B3V3XJ2W8G]].\nSchemes were introduced by Alexander Grothendieck as the basic objects of algebraic geometry.\nThey include algebraic varieties over any field, and also objects such as $\\operatorname{Spec} \\Z$ that come from number theory.\nThey also allow nilpotent functions, which record multiplicities and infinitesimal information.\n\n## Explanations\n\n### L1 human\n\nA manifold is built by gluing open pieces of $\\R^n$; a scheme is built by gluing affine schemes, the spectra of rings.\nEach piece carries its own ring of functions, and the pieces agree where they overlap.\nThe projective line is the main small example.\nIt is glued from two copies of the affine line, with coordinates $t$ and $s$, along the rule $s = 1/t$ where both are nonzero.\nThe result is not an affine scheme, but every point has an affine neighbourhood.\n",
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