  We construct a 2-category of differential graded schemes. The local affine
models in this theory are differential graded algebras, which are graded
commutative with unit over a field of characteristic zero, are concentrated in
non-positive degrees and have perfect cotangent complex. Quasi-isomorphic
differential graded algebras give rise to 2-isomorphic differential graded
schemes and a differential graded algebra can be recovered up to
quasi-isomorphism from the differential graded scheme it defines. Differential
graded schemes can be glued with respect to an etale topology and fibered
products of differential graded schemes correspond on the algebra level to
derived tensor products.
