nLab
derived elliptic curve

Idea

A derived elliptic curve is an object in higher geometry that is to an E-∞ ring as an ordinary elliptic curve is to an ordinary ring.

Definition

For the notation and terminology of the following definition, see (for the time being)

Let $A$ be an E-∞ ring. A derived elliptic curve over $A$ is derived group scheme $E\to \mathrm{Spec}A$ with the property that the underlying morphism $\overline{E}\to \mathrm{Spec}{\pi }_{0}A$ is an ordinary elliptic curve.

This is definition 4.1 in

• Jacob Lurie, A Survey of Elliptic Cohomology