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  "body": "\n## Summary\n\nThe Néron–Severi group of a smooth projective variety is the group of divisors modulo algebraic equivalence, equivalently the [[Picard group|3Z9DCWYXQZ]] modulo its identity component.\nThe theorem of the base, due to Severi over $\\C$ and Néron in general, says that it is a finitely generated abelian group.\nIts rank is the Picard number, and over $\\C$ it is the group of integral cohomology classes of type $(1, 1)$.\n\n## Explanations\n\n### L1 human\n\nThe Picard group of a variety can be huge, because line bundles come in continuous families.\nThe Néron–Severi group forgets the continuous part and keeps only the discrete data.\nOn an elliptic curve, line bundles are classified by their degree and a point of the curve; the Néron–Severi group keeps the degree only and is $\\Z$.\nOn a product of two curves, it also records how a divisor sits with respect to both factors.\n",
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