Authors: Fabien Morel and Vladimir Voevodsky
Title: A^1-homotopy theory of schemes
Email: morel@math.polytechnique.fr, vladimir@math.ias.edu

In this paper we begin to develope a machinery which we call {\em
$\af$-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 affine line plays
the role of the unit interval.