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  "body": "\n## Summary\n\nA locally ringed space is a [[ringed space|KNDXDE7K8M]] in which the ring of germs of functions at each point is a [[local ring|MZ02BKPHJA]].\nThe unique maximal ideal of that local ring consists of the germs that \"vanish at the point\".\nSchemes, smooth manifolds and complex manifolds are all locally ringed spaces.\nThis is the common frame in which scheme theory is built.\n\n## Explanations\n\n### L1 human\n\nThink of a space together with a rule that says which functions are allowed on each open set.\nAt a single point, one looks at the allowed functions near the point, where two functions count as the same if they agree near the point.\nFor a smooth manifold and a point $p$, such a germ $g$ is invertible exactly when $g(p) \\ne 0$.\nSo the germs that are not invertible are those with $g(p) = 0$, and they form one ideal; this is what \"local ring\" means.\nA locally ringed space is a space where this holds at every point.\n",
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