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  "body": "\n## Summary\n\nAn elliptic cohomology theory is a [[generalized cohomology theory|H28PSZR7XG]] whose [[formal group law|TNHP7XXYZT]] comes from an [[elliptic curve|427N6S6QQW]].\nOrdinary cohomology corresponds to the additive group and complex K-theory to the multiplicative group; elliptic curves are the next family of one-dimensional group varieties.\nElliptic cohomology theories detect height $2$ phenomena in chromatic homotopy theory.\nThey are tied to elliptic genera of manifolds and to [[topological modular forms|JN73KE96YB]].\n\n## Explanations\n\n### L1 human\n\nMany cohomology theories come with a rule for adding Chern classes of line bundles, given by a power series.\nFor ordinary cohomology the rule is plain addition, and for K-theory it is like multiplication.\nElliptic curves are curves that also carry an addition law, and near the identity this law is a power series too.\nAn elliptic cohomology theory is one whose rule is the addition law of an elliptic curve.\nSuch theories see more of the stable homotopy groups of spheres than K-theory does.\n",
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