The work of Vladimir Voevodsky

Abstract

Vladimir Voevodsky was born in 1966. He studied at Moscow State University and Harvard university. He is now Professor at the Institute for Advanced Study in Princeton. Among his main achievements are the following: he defined and developed motivic cohomology and the ${\mathbf A}^1$-homotopy theory of algebraic varieties; he proved the Milnor conjectures on the $K$-theory of fields. This article is a brief introduction to this work, for which Voevodsky was awarded the Fields Medal.