Work
Voevodsky's work is in the intersection of algebraic geometry with algebraic topology. Along with Fabien Morel, Voevodsky introduced a homotopy theory for schemes. He also formulated what is now believed to be the correct form of motivic cohomology, and used this new tool to prove Milnor's conjecture relating the Milnor K-theory of a field to its étale cohomology. For the above, he received the Fields Medal, together with Laurent Lafforgue, at the 24th International Congress of Mathematicians held in Beijing, China.
He is coauthor (with Andrei Suslin and Eric M. Friedlander) of Cycles, Transfers and Motivic Homology Theories, which develops the theory of motivic cohomology in some detail.
In January 2009, at an IHES anniversary conference for Alexander Grothendieck, Voevodsky announced a proof of the full Bloch-Kato conjectures.
Read more about this topic: Vladimir Voevodsky
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