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  "body": "\n## Summary\n\nAn algebraic cycle on a variety $X$ is a finite formal sum, with integer coefficients, of irreducible closed subvarieties of $X$.\nCycles of codimension one are the [[Weil divisors|Z9DN23DAE2]].\nCycles modulo [[rational equivalence|K76N026JFK]] form the [[Chow groups|EBEF6PEK4N]], the basic objects of [[intersection theory|4HV4WTAX9P]].\nThe question of which cohomology classes come from cycles is the subject of the [[Hodge conjecture|XAEEDWV3PM]] and of the [[standard conjectures|D8GA2R3QT5]].\n\n## Explanations\n\n### L1 human\n\nA cycle is a list of subvarieties, each with a whole number attached, such as \"two copies of this curve minus one copy of that curve\".\nCycles let one add and subtract subvarieties as if they were numbers.\nFor example, a line in the plane usually meets a cubic curve in the cycle $[P] + [Q] + [R]$ of three points.\nIf the line is tangent to the cubic at $P$, the intersection is $2[P] + [R]$.\nThe coefficients record multiplicities in this way.\n",
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