Alma mater Leningrad University | Name Alexander Merkurjev | |
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Native name Aleksandr Sergeyevich Merkurjev Institutions University of California Los Angeles Doctoral students Vladimir Khalin, MIkhail Gruntovich, Roman Bogomolov, Oleg Izhboldin, Nikita Karpenko Known for Merkurjev–Suslin theorem, cohomological invariants, canonical dimension, book of involutions, essential dimension Education Saint Petersburg State University Books Cohomological Invariants in Galois Cohomology, The Algebraic and Geometric Theory of Quadratic Forms Awards Guggenheim Fellowship for Natural Sciences, US & Canada | ||
Doctoral advisor Anatoli Yakovlev Residence United States of America | ||
Voevodsky proof of Milnor and Bloch-Kato conjectures - Alexander Merkurjev
Aleksandr Sergeyevich Merkurjev (Russian: Алекса́ндр Сергее́вич Мерку́рьев, born September 25, 1955) is a Russian-born American mathematician, who has made major contributions to the field of algebra. Currently Merkurjev is a professor at the University of California, Los Angeles.
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Work
Merkurjev's work focuses on algebraic groups, quadratic forms, Galois cohomology, algebraic K-theory and central simple algebras. In the early 1980s Merkurjev proved a fundamental result about the structure of central simple algebras of period dividing 2, which relates the 2-torsion of the Brauer group with Milnor K-theory. In subsequent work with Suslin this was extended to higher torsion as the Merkurjev–Suslin theorem. The full statement of the norm residue isomorphism theorem (also known as the Bloch-Kato conjecture) was proven by Voevodsky.
In the late 1990s Merkurjev gave the most general approach to the notion of essential dimension, introduced by Buhler and Reichstein, and made fundamental contributions to that field. In particular Merkurjev determined the essential p-dimension of central simple algebras of degree
Awards
Merkurjev won the Young Mathematician Prize of the Petersburg Mathematical Society for his work on algebraic K-theory. In 1986 he was an invited speaker at the International Congress of Mathematicians in Berkeley, California, and his talk was entitled "Milnor K-theory and Galois cohomology". In 1995 he won the Humboldt Prize, an international prize awarded to renowned scholars. Merkurjev gave a plenary talk at the 2nd European Congress of Mathematics in Budapest, Hungary in 1996. In 2012 he won the Cole Prize in Algebra for his work on the essential dimension of groups.
In 2015 a special volume of Documenta Mathematica was published in honor of Merkurjev's sixtieth birthday.