Alexander Merkurjev
| Alexander Merkurjev | |
|---|---|
| Native name | Aleksandr Sergeyevich Merkurjev |
| Born |
September 25, 1955 Saint Petersburg, USSR |
| Residence | United States |
| Fields | Mathematics |
| Institutions | University of California Los Angeles |
| Alma mater | Leningrad University |
| Doctoral advisor | Anatoli Yakovlev |
| 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 |
| Notable awards |
Cole Prize in Algebra (2012) Petersburg Mathematical Society Prize (1982) |
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.
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, recently generalized in the norm residue isomorphism theorem (previously known as the Bloch-Kato conjecture), proven in full generality by Rost and 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 (for a prime p) and, in joint work with Karpenko, the essential dimension of finite p-groups.
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