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  "body": "\n## Summary\n\nThe spectrum $\\operatorname{Spec} R$ of a [[commutative ring|0310REJJY8]] $R$ is the set of its [[prime ideals|00MHHZ9SNE]], with the [[Zariski topology|8SQK7RTB63]].\nIt turns a ring into a geometric space, on which the elements of $R$ behave like functions.\nA ring homomorphism $R \\to A$ gives a continuous map $\\operatorname{Spec} A \\to \\operatorname{Spec} R$ in the opposite direction.\nThe spectrum is the underlying space of an affine scheme, the basic object of modern algebraic geometry.\n\n## Explanations\n\n### L1 human\n\nFor the integers, the points of $\\operatorname{Spec} \\Z$ are the ideals $(2), (3), (5), \\ldots$, one for each prime number, and one extra point $(0)$.\nAn integer $n$ \"vanishes\" at the point $(p)$ when $p$ divides $n$, so a nonzero integer $n$ behaves like a function with finitely many zeros.\nFor the polynomial ring $\\C[x]$, the maximal ideals $(x - a)$ correspond to the complex numbers $a$, so the spectrum contains a copy of the complex line.\nThe [[definition|QJAXM2SF1Z]] gives the set and its topology.\n",
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