A commutative group -scheme over is an (∞,1)-functor
This is (adapted from) definition 3.1 of
warning careful, this needs a bit more attention. The general idea is obvious, but the detaisl require care. One problem is that in the Elliptic Survey “derived scheme” really referes to Spectral Schemes, which isn’t available yet, and not to the derived schemes discussed in Structured Spaces.
An important special case is that of a derived elliptic curve.