Vladimir Voevodsky (Russian: Владимир Александрович Воеводский, born 4 June 1966) is a Russian mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002.
Vladimir Voevodsky's father, Aleksandr Voevodsky, was head of the Laboratory of High Energy Leptons in the Institute for Nuclear Research at the Russian Academy of Sciences. His mother is a chemist. Voevodsky attended Moscow State University and received his Ph.D. in mathematics from Harvard University in 1992, advised by David Kazhdan. Currently he is a full professor at the Institute for Advanced Study in Princeton, New Jersey.
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.
- Friedlander, Eric M., Rapoport, Michael, and Suslin, Andrei. (2003) "The mathematical work of the 2002 Fields medalists". Notices Amer. Math. Soc. 50 (2), 212–217.
- Voevodsky, Vladimir, Suslin, Andrei, and Friedlander, Eric M. (2000) Cycles, transfers, and motivic homology theories. Annals of Mathematics Studies Vol. 143. Princeton University Press.
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