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  "body": "\n## Summary\n\nAn affine scheme is the [[spectrum|FB45BHHA2J]] $\\operatorname{Spec} A$ of a [[commutative ring|0310REJJY8]] $A$, made into a [[locally ringed space|B7FPT8JTXR]] by its structure sheaf.\nEvery commutative ring gives one, and the ring can be read back as the ring of global functions.\nAffine schemes are the local building blocks of all [[schemes|5A35TYZD02]], just as open balls are the local pieces of manifolds.\n\n## Explanations\n\n### L1 human\n\nAn affine scheme turns a ring into a geometric object.\nIts points are the prime ideals of the ring, and the elements of the ring act as functions on these points.\nFor the polynomial ring $\\C[x, y]$, the maximal ideals $(x - a, y - b)$ are the points $(a, b)$ of the complex plane, and other primes, such as $(y - x^2)$, stand for whole curves.\nThe structure sheaf records which fractions are allowed as functions on each open set.\n",
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