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  "body": "\n## Summary\n\nA Cartier divisor on a [[scheme|5A35TYZD02]] is a hypersurface described locally by one equation.\nThe local equations are given up to multiplication by invertible functions.\nEach Cartier divisor determines an [[invertible sheaf|7JCF2TE3V5]], and on an integral scheme every invertible sheaf arises this way.\nSo the classes of Cartier divisors give the [[Picard group|3Z9DCWYXQZ]] of an integral scheme.\nOn a Noetherian integral separated scheme whose local rings are factorial, Cartier divisors are the same as [[Weil divisors|Z9DN23DAE2]].\nCartier divisors are the right kind of divisor on singular schemes, where Weil divisors and line bundles no longer match.\n\n## Explanations\n\n### L1 human\n\nOn a curve, a divisor is a finite list of points with integer multiplicities.\nA Cartier divisor records this through local functions: near each point you give a rational function whose zeros and poles have the desired orders.\nTwo local functions that differ by a nowhere vanishing function describe the same divisor there.\nFor example, on the affine line with coordinate $t$, the single function $t^2$ describes the point $0$ counted twice.\nThe function $t^2(t-1)^{-1}$ describes the point $0$ counted twice minus the point $1$.\n",
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