DOCUMENTA MATHEMATICA, Extra Volume ICM I (1998), 579-604

Vladimir Voevodsky

Title: ${\bf A}^1$-Homotopy Theory

${\bf A}^1$-homotopy theory is the homotopy theory for algebraic varieties and schemes which uses the affine line as a replacement for the unit interval. In the paper I present in detail the basic constructions of the theory following the sequence familiar from standard texbooks on algebraic topology. At the end I define motivic cohomology and algebraic cobordisms and describe algebraic K-theory in terms of this theory.

1991 Mathematics Subject Classification:

Keywords and Phrases:

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