Alexander Merkurjev

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Merkurjev in Oberwolfach 2009

Alexander S. Merkurjev ( Russian Александр Сергеевич Меркурьев , Alexander Sergejewitsch Merkurjew ; born September 25, 1955 ) is a Russian -born American mathematician who deals with algebra .

Merkurjev received his doctorate in 1979 under Anatoly Jakowlew at the University of Leningrad . In 1982 he won the Prize for Young Mathematicians of the Leningrad Mathematical Society and was a professor at Leningrad University. In the 1990s he went to the USA and became a professor at the University of California, Los Angeles .

Merkurjev deals with algebraic groups, quadratic forms, Galois cohomology , algebraic K-theory , theory of algebras. In 1981 he proved a fundamental theorem on the structure of centrally simple division algebras, expanded shortly afterwards in collaboration with Andrei Suslin . These and other works by Merkurjev and Suslin were important in the run-up to Vladimir Voivodski's proof of the Milnor conjecture and the Bloch-Kato conjecture (on the Galoisohomological description of higher Milnor K groups) and provided the motivation for the introduction of the norm important in Voivodski's proof -Varietas. Merkurjev's work from 1982 proved a special case of the Bloch-Kato conjecture and his work with Suslin in the 1980s proved other special cases. For his theorem from 1982, Merkurjev later also found “elementary” proofs without using algebraic K-theory.

With J. Buhler and Z. Reichstein he introduced new invariants of algebraic structures called “Essential Dimension”.

In 1996 he gave one of the plenary lectures at the European Congress of Mathematicians in Budapest ( K-theory and algebraic groups ) and was invited speaker at the ECM in Paris 1992 (Algebraic K-theory and Galois cohomology). In 2012 he received the Cole Prize in Algebra. In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley ( Milnor K-theory and Galois cohomology ). He is a fellow of the American Mathematical Society .

Fonts

  • with Max-Albert Knus , Markus Rost , Jean-Pierre Tignol: The book of involutions, American Mathematical Society 1998
  • with Skip Garibaldi, Jean-Pierre Serre : Cohomological Invariants in Galois Cohomology, American Mathematical Society 2003
  • with Richard Ellman, Nikita Karpenko: Algebraic and geometric theory of quadratic forms, American Mathematical Society 2008

Web links

Individual evidence

  1. ↑ Merkurjev On the norm residue symbol of degree 2 , Russian, Doklady Akad. Nauk SSR, Vol. 261, 1981, p. 542
  2. ↑ The Merkurjev-Suslin theory is presented, for example, in Philippe Gille, Tamas Szamuely Central simple algebras and Galois cohomology , Cambridge University Press 2006. The original work is Merkurjev, Suslin K-cohomology of Severi-Brauer varieties and the norm-residue homomorphism , Math. USSR Izvestija Vol. 21, 1983, p. 307, Russian Izv.Akad.Nauk USSR Vol. 46, 1982, p. 1011. Simplifications in the proof were provided by Merkurjev of fields and the Brauer Group , in Spencer Bloch (editor ) Applications of K-theory to algebraic geometry and number theory , Contemporary Mathematics Vol. 55/1, 1986, p. 529
personal data
SURNAME Merkurjev, Alexander
ALTERNATIVE NAMES Меркурьев, Александр Сергеевич (Russian spelling); Merkurjew, Alexander Sergejewitsch (German transcription); Merkurjev, Alexander Sergejevich (English transcription)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH September 25, 1955