Holmstrom Functor of points

See Toen Essen talk for an introduction, and conditions on a functor to be a scheme. Section 1.3 in particular.

http://ncatlab.org/nlab/show/functor+of+points

http://mathoverflow.net/questions/52458/comprehensive-and-self-contained-treatment-of-algebraic-geometry-using-functor-of

http://mathoverflow.net/questions/16832/functorial-point-of-view-of-spectrum-looking-for-reference

http://mathoverflow.net/questions/33070/functorial-point-of-view-for-formal-schemes

nLab page on Functor of points