A^1-homotopy theory of schemes, by Fabien Morel and Vladimir Voevodsky

In this paper we begin to develope a machinery which we call A^1-homotopy theory of schemes. All our constructions are based on the intuitive feeling that if the category of algebraic varieties is in any way similar to the category of topological spaces then there should exist a homotopy theory of algebraic varieties where the affine line plays the role of the unit interval.

Fabien Morel <morel@math.polytechnique.fr>
Vladimir Voevodsky <vladimir@math.ias.edu>