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  "body": "\n## Summary\n\nA coherent sheaf on a Noetherian scheme is a quasi-coherent sheaf that is locally given by finitely generated modules.\nCoherent sheaves are the algebraic analogue of finite-dimensional data: on a proper scheme over a field, their cohomology groups are finite-dimensional.\nThey include vector bundles, ideal sheaves of closed subschemes, and structure sheaves of closed subschemes.\n\n## Explanations\n\n### L1 human\n\nA coherent sheaf is a quasi-coherent sheaf that is finite in each small region.\nOn an affine piece it is described by a finitely generated module, so by finitely many generators and relations.\nVector bundles are coherent, but coherent sheaves can also do things vector bundles cannot.\nFor example, the sheaf that has the value $k$ at the origin of a line and $0$ elsewhere is coherent, with a jump in rank at one point.\n",
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