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  "body": "\n## Summary\n\nRational equivalence is the finest of the usual equivalence relations on [[algebraic cycles|9VFWPZEVGN]].\nTwo cycles are rationally equivalent when their difference is a sum of divisors of rational functions on subvarieties.\nThe quotient of the group of cycles by rational equivalence is the [[Chow group|EBEF6PEK4N]].\n\n## Explanations\n\n### L1 human\n\nOn a curve, the zeros of a rational function minus its poles form a cycle of points that one wants to count as zero.\nRational equivalence declares all such cycles to be zero, and does the same on every subvariety of every dimension.\nOn the projective line, the function $(x - a)/(x - b)$ has a zero at $a$ and a pole at $b$, so any two points are rationally equivalent.\nOn an elliptic curve, two distinct points are never rationally equivalent, so the relation sees the geometry of the curve.\n",
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