[To be merged with .]
A general group scheme is a group object in generalized schemes: it is a generalization to higher geometry of a group scheme.
Let be a -generalized scheme for the geometry (for structured (β,1)-toposes) that defines the desired notion of derived schemes.
A commutative group -scheme over is an (β,1)-functor
from -schemes over to topological abelian groups, such that composition with the forgetful functor is representable by a derived scheme flat over .
This is (adapted from) definition 3.1 of
warning careful, this needs a bit more attention. The general idea is obvious, but the details require care. One problem is that in the Elliptic Survey βderived schemeβ really refers to Spectral Schemes and not to the derived schemes discussed in Structured Spaces.
An important special case is that of a derived elliptic curve.
Last revised on December 23, 2016 at 10:09:18. See the history of this page for a list of all contributions to it.