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  "body": "\n## Summary\n\nThe residue field $\\kappa(x)$ of a point $x$ of a [[scheme|5A35TYZD02]] is the [[residue field|NJ3APQ8BHH]] of the local ring of the scheme at $x$.\nIt is the field in which functions near $x$ take their \"value at $x$\".\nDifferent points of one scheme can have residue fields of different characteristics, as for $\\operatorname{Spec} \\Z$.\n\n## Explanations\n\n### L1 human\n\nOn a variety over the complex numbers, the value of a polynomial at a point is a complex number.\nOn a scheme, the value of a function at a point lives in the residue field of that point, and this field can change from point to point.\nOn $\\operatorname{Spec} \\Z$, an integer $n$ has value $n \\bmod p$ at the point $(p)$, in the field with $p$ elements.\nAt the point $(0)$ its value is $n$ itself, in the field $\\Q$.\n",
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  "name": "Residue field of a point",
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